Course: 9.12 增加和减减与异式排减器不同的逻辑表达式

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与不同排引符添加和减减逻辑表达式
One part of a line segment measures $\begin{align*}\frac{3}{x-2}\end{align*}$ . The other part of the segment measures $\begin{align*}\frac{2}{x+1}\end{align*}$ . What is the total length of the line segment?
::一条线段的一个部分是3x-2。另一部分是2x+1。线段的总长度是多少?

Adding and Subtracting Rational Expressions
::添加和减减理性表达式

Now, we will add two rational expressions where were you will have to multiply both fractions by a constant in order to get the Lowest Common Denominator or LCD. Recall how to add fractions where the denominators are not the same.
::现在,我们将添加两个合理的表达式, 您需要将两个分数乘以一个常数, 才能获得最低的常见分数或 LCD 。回顾如何在分数不同的地方添加分数。

$\begin{align*}\frac{4}{15} + \frac{5}{18}\end{align*}$

Find the LCD. $\begin{align*}15=3 \cdot 5\end{align*}$ and $\begin{align*}18=3 \cdot 6\end{align*}$ . So, they have a common factor of 3. Anytime two denominators have a common factor, it only needs to be listed once in the LCD. The LCD is therefore $\begin{align*}3 \cdot 5 \cdot 6=90\end{align*}$ .
::查找LCD. 15=35和18=36. 因此,它们有一个共同系数3。任何时候,两个分母都有共同系数,只需在LCD上列出一次。因此,LCD是 356=90。

$\begin{aligned} \frac{4}{15} + \frac{5}{18} & = \frac{4}{3 \cdot 5} + \frac{5}{3 \cdot 6} \\ = \frac{6}{6} \cdot \frac{4}{3 \cdot 5} + \frac{5}{3 \cdot 6} \cdot \frac{5}{5} \\ = \frac{24}{90} + \frac{25}{90} \\ = \frac{49}{90} \end{aligned}$
$\begin{align*}\frac{4}{15} + \frac{5}{18} &= \frac{4}{3 \cdot 5} + \frac{5}{3 \cdot 6} \\ &= {\color{red}\frac{6}{6}} \cdot \frac{4}{3 \cdot 5} + \frac{5}{3 \cdot 6} \cdot {\color{blue}\frac{5}{5}} \\ &= \frac{24}{90} + \frac{25}{90}\\ &= \frac{49}{90}\end{align*}$

We multiplied the first fraction by $\begin{align*}\frac{6}{6}\end{align*}$ to obtain 90 in the denominator. Recall that a number over itself is $\begin{align*}6 \div 6=1\end{align*}$ . Therefore, we haven’t changed the value of the fraction. We multiplied the second fraction by $\begin{align*}\frac{5}{5}\end{align*}$ . We will now apply this idea to rational expressions.
::我们将第一个分数乘以66 以获得分母中的 90 。回顾一个数字本身是 66=1 。因此,我们没有改变这个分数的值。我们将第二个分数乘以55 。我们现在将把这个想法应用到理性表达中。

Let's a dd or subtract the following rational expressions.
::我们加或减以下合理表达式。

Add $\begin{align*}\frac{x+5}{x^2-3x} + \frac{3}{x^2+2x}\end{align*}$ .
::添加 x+5x2-3x+3x2+2x。

First factor each denominator to find the LCD. The first denominator, factored, is $\begin{align*}x^2-3x=x(x-3)\end{align*}$ . The second denominator is $\begin{align*}x^2+2x=x(x+2)\end{align*}$ . Both denominators have and $\begin{align*}x\end{align*}$ , so we only need to list it once. The LCD is $\begin{align*}x(x-3)(x+2)\end{align*}$ .
::找到液晶体体的第一个分母。第一个分母是 x2 - 3x=x(x- 3),第二个分母是 x2+2x=x(x+2),两个分母都有和 x,所以我们只需要列出一次。LCD是 x(x-3)(x+2) 。

$\begin{align*}\frac{x+5}{x^2-3x} + \frac{3}{x^2+2x} = \frac{x+5}{x(x-3)} + \frac{3}{x(x+2)}\end{align*}$
::x+5x2 - 3x+3x2+2x=x+5x(x-3)+3x(x+2)

Looking at the two denominators factored, we see that the first fraction needs to be multiplied by $\begin{align*}\frac{x+2}{x+2}\end{align*}$ and the second fraction needs to be multiplied by $\begin{align*}\frac{x+3}{x+3}\end{align*}$ .
::查看所考虑的两个分母,我们看到第一个分母需要乘以 x+2x+2,第二个分母需要乘以 x+3x+3。

$\begin{aligned} = \frac{x + 2}{x + 2} \cdot \frac{x + 5}{x (x - 3)} + \frac{3}{x (x + 2)} \cdot \frac{x - 3}{x - 3} \\ = \frac{(x + 2) (x + 5) + 3 (x - 3)}{x (x + 2) (x - 3)} \end{aligned}$
$\begin{align*}&= {\color{red}\frac{x+2}{x+2}} \cdot \frac{x+5}{x{\color{blue}(x-3)}} + \frac{3}{x{\color{red}(x+2)}} \cdot {\color{blue}\frac{x-3}{x-3}} \\ &= \frac{(x+2)(x+5)+3(x-3)}{x{\color{red}(x+2)} {\color{blue}(x-3)}}\end{align*}$
::=x+2x+2x+2xx+5x(x-3)+3x(x+2)xx-3x-3x=(x+2)(x+5)+3(x-3)xx(x+2)xx(x+2)x(x+2)(x-3)x(x+2)(x-3)

At this point, we need to FOIL the first expression and distribute the 3 to the second. Lastly we need to combine like terms .
::此时此刻,我们需要FOIL第一种表达方式,将第三种表达方式分发到第二种,最后,我们需要将类似术语结合起来。

$\begin{aligned} = \frac{x^{2} + 7 x + 10 + 3 x - 9}{x (x + 2) (x - 3)} \\ = \frac{x^{2} + 10 x + 1}{x (x + 2) (x - 3)} \end{aligned}$
$\begin{align*}&= \frac{x^2+7x+10+3x-9}{x(x+2)(x-3)} \\ &= \frac{x^2+10x+1}{x(x+2)(x-3)}\end{align*}$
::=x2+7x+10+3x-9x(x+2)(x-3)=x2+10x+1x(x+2)(x-3)

The quadratic in the numerator is not factorable, so we are done.
::分子中的二次曲线是不可计数的,所以我们完成了。

Add $\begin{align*}\frac{4}{x+6} + \frac{x-2}{3x+1}\end{align*}$ .
::添加 4x+6+x-23x+1。

The denominators have no common factors, so the LCD will be $\begin{align*}(x+6)(3x+1)\end{align*}$ .
::这些分母没有共同的因素,所以液晶晶体将(x+6)(3x+1)。

$\begin{aligned} \frac{4}{x + 6} + \frac{x - 2}{3 x + 1} & = \frac{3 x + 1}{3 x + 1} \cdot \frac{4}{x + 6} + \frac{x - 2}{3 x + 1} \cdot \frac{x + 6}{x + 6} \\ = \frac{4 (3 x + 1)}{(3 x + 1) (x + 6)} + \frac{(x - 2) (x + 6)}{(3 x + 1) (x + 6)} \\ = \frac{12 x + 4 + x^{2} + 4 x - 12}{(3 x + 1) (x + 6)} \\ = \frac{x^{2} + 16 x - 8}{(3 x + 1) (x + 6)} \end{aligned}$
$\begin{align*}\frac{4}{x+6} + \frac{x-2}{3x+1} &= {\color{red}\frac{3x+1}{3x+1}} \cdot \frac{4}{{\color{blue}x+6}} + \frac{x-2}{{\color{red}3x+1}} \cdot {\color{blue}\frac{x+6}{x+6}} \\ &= \frac{4(3x+1)}{{\color{red}(3x+1)}{\color{blue}(x+6)}} + \frac{(x-2)(x+6)}{{\color{red}(3x+1)} {\color{blue}(x+6)}} \\ &= \frac{12x+4+x^2+4x-12}{{\color{red}(3x+1)} {\color{blue}(x+6)}} \\ &= \frac{x^2+16x-8}{(3x+1)(x+6)}\end{align*}$
::4x+6+6+x-23x+1=3x+13x+13x+1}4x+6+x-23x+1*4x+6x+6=4(3x+1)(3x+1)(3x+1)(x+1)(x+6)+(x-2(x+6)(3x)(3x+1)(x+1)(x+6)=12x+4+x2+x2+4x4(3x+1)(x+6)=x2+16x8(3x+1)(x+6)

Subtract $\begin{align*}\frac{x-1}{x^2+5x+4} - \frac{x+2}{2x^2+13x+20}\end{align*}$ .
::减号 x-1x2+5x+4-x+22x2+13x+20。

To find the LCD, we need to factor the denominators.
::要找到液晶,我们需要考虑分母

$\begin{aligned} x^{2} + 5 x + 4 & = (x + 1) (x + 4) \\ 2 x^{2} + 13 x + 20 & = (2 x + 5) (x + 4) \\ L C D & = (x + 1) (2 x + 5) (x + 4) \end{aligned}$
$\begin{align*}x^2+5x+4 &= {\color{red}(x+1)} {\color{green}(x+4)} \\ 2x^2+13x+20 &= {\color{blue}(2x+5)} {\color{green}(x+4)} \\ LCD &= {\color{red}(x+1)} {\color{blue}(2x+5)} {\color{green}(x+4)}\end{align*}$
::x2+5x+4=(x+1)(x+4)(x+4)2x2+13x+20=(2x+5)(x+4)LCD=(x+1)(2x+5)(x+4)

$\begin{aligned} \frac{x - 1}{x^{2} + 5 x + 4} - \frac{x + 2}{2 x^{2} + 13 x + 20} & = \frac{x - 1}{(x + 1) (x + 4)} - \frac{x + 2}{(2 x + 5) (x + 4)} \\ = \frac{2 x + 5}{2 x + 5} \cdot \frac{x - 1}{(x + 1) (x + 4)} - \frac{x + 2}{(2 x + 5) (x + 4)} \cdot \frac{x + 1}{x + 1} \\ = \frac{(2 x + 5) (x - 1) - (x + 2) (x + 1)}{(x + 1) (2 x + 5) (x + 4)} \\ = \frac{2 x^{2} + 3 x - 5 - (x^{2} + 3 x + 2)}{(x + 1) (2 x + 5) (x + 4)} \\ = \frac{2 x^{2} + 3 x - 5 - x^{2} - 3 x - 2}{(x + 1) (2 x + 5) (x + 4)} \\ = \frac{x^{2} - 7}{(x + 1) (2 x + 5) (x + 4)} \end{aligned}$
$\begin{align*}\frac{x-1}{x^2+5x+4} - \frac{x+2}{2x^2+13x+20} &= \frac{x-1}{{\color{red}(x+1)} {\color{green}(x+4)}} - \frac{x+2}{{\color{blue}(2x+5)}(x+4)} \\ &= {\color{blue}\frac{2x+5}{2x+5}} \cdot \frac{x-1}{{\color{red}(x+1)}{\color{green}(x+4)}} - \frac{x+2}{{\color{blue}(2x+5)}{\color{green}(x+4)}} \cdot {\color{red}\frac{x+1}{x+1}} \\ &= \frac{(2x+5)(x-1)-(x+2)(x+1)}{{\color{red}(x+1)}{\color{blue}(2x+5)}{\color{green}(x+4)}} \\ &= \frac{2x^2+3x-5-(x^2+3x+2)}{(x+1)(2x+5)(x+4)} \\ &= \frac{2x^2+3x-5-x^2-3x-2}{(x+1)(2x+5)(x+4)} \\ &= \frac{x^2-7}{(x+1)(2x+5)(x+4)}\end{align*}$
::x - 1x2+5x+4x+4x+4x+4x+4x+2x2x2x2xx+5(x+4)=2x+52x+5x2(2x+4)=2x+52x+5x1x1(x1+1x+4)x+2+2x5(x+4x+4x+4x4x4x4x+4x4x4x+4x+4x2x+2x2x2+2x2x+5)(x1x+5)(2x+4)=2x+52x+5x+5x-2x-2x-3x-2x-3x2(x2x+5)(x2x+5)(x+2x+2x+5)(x+4)x=x2x7(x+1)(2x+5)(2x+5)(x+4)

Examples
::实例

Example 1
::例1

Earlier, you were asked to find the total length of the line segment.
::早些时候,有人要求你找到线段的总长度。

We need to add the two parts of the segment to get the whole.
::我们需要增加这部分的两部分,以取得整个结果。

$\begin{align*}\frac{3}{x-2} + \frac{2}{x+1}\end{align*}$
::3x-2+2x+1

The denominators have no common factors, so the LCD will be $\begin{align*}(x-2)(x+1)\end{align*}$ .
::这些分母没有共同的因素,所以液晶晶体将(x-2)(x+1)。

$\begin{aligned} \frac{3}{x - 2} + \frac{2}{x + 1} & = \frac{x + 1}{x + 1} \cdot \frac{3}{x - 2} + \frac{2}{x + 1} \cdot \frac{x - 2}{x - 2} \\ = \frac{3 (x + 1)}{(x + 1) (x - 2)} + \frac{(2) (x - 2)}{(x + 1) (x - 2)} \\ = \frac{3 x + 3 + 2 x - 4}{(x + 1) (x - 2)} \\ = \frac{5 x - 1}{(x + 1) (x - 2)} \end{aligned}$
$\begin{align*}\frac{3}{x-2} + \frac{2}{x+1} &= {\color{red}\frac{x+1}{x+1}} \cdot \frac{3}{{\color{blue}x-2}} + \frac{2}{{\color{red}x+1}} \cdot {\color{blue}\frac{x-2}{x-2}} \\ &= \frac{3(x+1)}{{\color{red}(x+1)}{\color{blue}(x-2)}} + \frac{(2)(x-2)}{{\color{red}(x+1)} {\color{blue}(x-2)}} \\ &= \frac{3x+3+2x-4}{{\color{red}(x+1)} {\color{blue}(x-2)}} \\ &= \frac{5x-1}{(x+1)(x-2)}\end{align*}$
::3x-2+2x+2x+1x1=x+1x1x1x1=1x1x1x3x2+2x2x1x-2x3(x+1)(x+1)(x+1)(x1)(x-2)+(2)x-2(x-2)(x-2)(x-1)(x-2)=3x+3+2+2x4(x+1)(x-2)=5x-1(x+1)(x-2)

Therefore, the total length of the line segment is $\begin{align*}\frac{5x-1}{(x+1)(x-2)}\end{align*}$ .
::因此,直线段的总长度为5x-1(x+1)(x-2)。

Perform the indicated operation .
::执行指示的操作。

Example 2
::例2

$\begin{align*}\frac{3}{x^2-6x} + \frac{5-x}{2x-12}\end{align*}$
::3x2-6x+5-x2x-12

The LCD is $\begin{align*}3x(x-6)\end{align*}$ .
::LCD为3x(x-6) 。

$\begin{aligned} \frac{3}{x^{2} - 6 x} + \frac{5 - x}{2 x - 12} & = \frac{2}{2} \cdot \frac{3}{x (x - 6)} + \frac{5 - x}{2 (x - 6)} \cdot \frac{x}{x} \\ = \frac{6 + x (5 - x)}{2 x (x - 6)} \\ = \frac{6 + 5 x - x^{2}}{2 x (x - 6)} \\ = \frac{- 1 (x^{2} - 5 x - 6)}{2 x (x - 6)} \end{aligned}$
$\begin{align*}\frac{3}{x^2-6x} + \frac{5-x}{2x-12} &= \frac{2}{2} \cdot \frac{3}{x(x-6)} + \frac{5-x}{2(x-6)} \cdot \frac{x}{x} \\ &= \frac{6+x(5-x)}{2x(x-6)} \\ &= \frac{6+5x-x^2}{2x(x-6)} \\ &= \frac{-1(x^2-5x-6)}{2x(x-6)}\end{align*}$
::3x2 - 6x+5 - x2x - 6x- 6- 6x= 2x3x(x-6)+5-xx2(x-6)xxx=6x(5-xx)2x(x-6)=6+5x-x2x(x-6)x(x-6)x*1(x2-5x-6)2x(x-6)x

We pulled a -1 out of the numerator so we can factor it.
::我们从分子中取出一个 -1,这样我们就可以计算出来。

$\begin{aligned} = \frac{- 1 (x - 6) (x + 1)}{2 x (x - 6)} \\ = \frac{- x - 1}{2 x} \end{aligned}$
$\begin{align*}&= \frac{-1 \bcancel{(x-6)}(x+1)}{2x \bcancel{(x-6)}} \\ &= \frac{-x-1}{2x}\end{align*}$
::1(x- 6)(x+1) 2x(x-6) x- 12x

Example 3
::例3

$\begin{align*}\frac{x}{x^2+4x+4} - \frac{x-5}{x^2+5x+6}\end{align*}$
::x2+4x+4-4-x-5x2+5x6

The LCD is $\begin{align*}(x+2)(x+2)(x+3)\end{align*}$ .
::液晶显示器为(x+2)(x+2)(x+2)(x+3)。

$\begin{aligned} \frac{x}{x^{2} + 4 x + 4} - \frac{x - 5}{x^{2} + 5 x + 6} & = \frac{x + 3}{x + 3} \cdot \frac{x}{(x + 2) (x + 2)} - \frac{x - 5}{(x + 2) (x + 3)} \cdot \frac{x + 2}{x + 2} \\ = \frac{x (x + 3) - (x - 5) (x + 2)}{(x + 2) (x + 2) (x + 3)} \\ = \frac{x^{2} + 3 x - (x^{2} - 3 x - 10)}{(x + 2)^{2} (x + 3)} \\ = \frac{x^{2} + 3 x - x^{2} + 3 x + 10}{(x + 2)^{2} (x + 3)} \\ = \frac{6 x + 10}{(x + 2)^{2} (x + 3)} \\ = \frac{2 (3 x + 5)}{(x + 2)^{2} (x + 3)} \end{aligned}$
$\begin{align*}\frac{x}{x^2+4x+4} - \frac{x-5}{x^2+5x+6} &= \frac{x+3}{x+3} \cdot \frac{x}{(x+2)(x+2)} - \frac{x-5}{(x+2)(x+3)} \cdot \frac{x+2}{x+2} \\ &= \frac{x(x+3)-(x-5)(x+2)}{(x+2)(x+2)(x+3)} \\ &= \frac{x^2+3x-(x^2-3x-10)}{(x+2)^2(x+3)} \\ &= \frac{x^2+3x-x^2+3x+10}{(x+2)^2(x+3)} \\ &= \frac{6x+10}{(x+2)^2(x+3)} \\ &= \frac{2(3x+5)}{(x+2)^2(x+3)}\end{align*}$
::x2+4x+4x+4x-x5x2+5x6xx+3x3x3x3xxxxxxxxxxxx2+2(x+2)-x5(x+2)(x+3)(x+3)xxxxxxxxxxxxxxxxxxx5(x+2)(x+2(x2)(x+2)(x+2)(x+2)(x+2)(x+2)(x+2)(x+2)(x+2)(x+2)(x+2)(x+2)(x+2)(x+2x+2)(x+2)(x+2)(x+2)(x+2)(x+2)(x+2)(x+2)(x+3)(x+2)(x+2)(x+3)(x+3)(x+5)(x+3)(x+3)(x+2)(x+2)(x+2)(x+2)(xx)xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx=xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx=xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

Example 4
::例4

$\begin{align*}\frac{2x}{x^2-x-20} + \frac{x^2-9}{x^2-1}\end{align*}$
::2xx2 - x - x - 20+x2 - 9x2 - 1

The LCD is $\begin{align*}(x-5)(x+4)(x+1)(x-1)\end{align*}$ .
::致死剂量为(x-5)(x+4)(x+1)(x-1)(x-1/1)。

$\begin{aligned} \frac{2 x}{x^{2} - x - 20} + \frac{x^{2} - 9}{x^{2} - 1} & = \frac{(x + 1) (x - 1)}{(x + 1) (x - 1)} \cdot \frac{2 x}{(x - 5) (x + 4)} + \frac{x^{2} - 9}{(x + 1) (x - 1)} \cdot \frac{(x - 5) (x + 4)}{(x - 5) (x + 4)} \\ = \frac{2 x (x + 1) (x - 1) + (x^{2} - 9) (x - 5) (x + 4)}{(x - 5) (x + 4) (x + 1) (x - 1)} \\ = \frac{2 x^{3} - 2 x + x^{4} - x^{3} - 29 x^{2} + 9 x + 180}{(x - 5) (x + 4) (x + 1) (x - 1)} \\ = \frac{x^{4} + x^{3} - 29 x^{2} + 7 x + 180}{(x - 5) (x + 4) (x + 1) (x - 1)} \end{aligned}$
$\begin{align*}\frac{2x}{x^2-x-20} + \frac{x^2-9}{x^2-1} &= \frac{(x+1)(x-1)}{(x+1)(x-1)} \cdot \frac{2x}{(x-5)(x+4)} + \frac{x^2-9}{(x+1)(x-1)} \cdot \frac{(x-5)(x+4)}{(x-5)(x+4)} \\ &= \frac{2x(x+1)(x-1)+(x^2-9)(x-5)(x+4)}{(x-5)(x+4)(x+1)(x-1)} \\ &= \frac{2x^3-2x+x^4-x^3-29x^2+9x+180}{(x-5)(x+4)(x+1)(x-1)} \\ &= \frac{x^4+x^3-29x^2+7x+180}{(x-5)(x+4)(x+1)(x-1)}\end{align*}$
::2xx2-x-20+x2-9x2-1=(x+1)(x-1)(x-1)(x-1)(x-1)(x-1)(x-1)(x-1)(x+4)(x+4)+x2-9(x+1)(x+4)(x-5(x-5)(x-5)(x+4)(x-5)(x-4)(x-2)(x-5)(x-5)(x+4)(x+4)(x-1)(x-1)(x-1)(x-1)=2x3-2xx4(x4)-x3-x3(x5)(x+4)(x+4)(x+1)(x)(x-1)(x-1)(x)x4+1)(x4+3-292)(x)(x)(x1)(x1)(x4+3-x3-292)(x2)(x+7x)(x-5)(x-5)(x+5)(x+5)(x+4)(x+1)(x)(x-1)(x)

Review
::回顾

Find the LCD.
::找到液晶显示器

$\begin{align*}3x, \ 7x\end{align*}$
::3x, 7x

$\begin{align*}x-2, \ 2x-1\end{align*}$
::x-2, 2x-1

$\begin{align*}x^2 - 9, \ x^2-x-6\end{align*}$
::x2-9, x2-x-6

$\begin{align*}4x, \ x^2-6x\end{align*}$
::4x, x2-6x

$\begin{align*}x^2-4, \ x^2+4x+4, \ x^2+3x-10\end{align*}$
::x2-4, x2+4x+4, x2+3x-10

Perform the indicated operation.
::执行指示的操作。

$\begin{align*}\frac{5}{3x} + \frac{x}{2}\end{align*}$
::53x+x2

$\begin{align*}\frac{x+1}{x^2} - \frac{5}{7x}\end{align*}$
::x+1x2-57x

$\begin{align*}\frac{x-5}{4x} + \frac{3}{x+2}\end{align*}$
::x-54x+3x+2

$\begin{align*}\frac{5}{2x+6} + \frac{x-2}{x^2+2x-3}\end{align*}$
::52x+6+x-2x2+2x-3

$\begin{align*}\frac{4x+3}{2x^2+11x-6} - \frac{3x-1}{2x^2-x}\end{align*}$
::4x+32x2+11x-6-3x-12x2-x

$\begin{align*}\frac{x}{3x^2+x-2} - \frac{2}{15x-10}\end{align*}$
::x3x2+x-2-2-2-15x-10

$\begin{align*}\frac{3x}{x^2-3x-10} + \frac{x+1}{x^2-2x-15} - \frac{2}{x^2+5x+6}\end{align*}$
::3xx2-3x-3x-10+x1x2-2-2x-2-15-2x2+5x6

$\begin{align*}\frac{7+x}{x^2-2x} - \frac{x-6}{3x^2+5x} - \frac{x+4}{3x^2-x-10}\end{align*}$
::7+xx2-2x-x-x-x-63x2+5x-x-x-43x2-x-10

$\begin{align*}\frac{3x+2}{x^2-1} - \frac{10x-7}{5x^2+5x} + \frac{3}{x-1}\end{align*}$
::3x+2x2-1-10x-75x2+5x+3x-1

$\begin{align*}\frac{x+6}{2x-1} + \frac{2x}{3x+2} - \frac{5}{x}\end{align*}$
::x+62x-1+2x3x+2-5x

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Section outline

General

与不同排引符添加和减减逻辑表达式

Adding and Subtracting Rational Expressions ::添加和减减理性表达式

Examples ::实例

Example 1 ::例1

Example 2 ::例2

Example 3 ::例3

Example 4 ::例4

Review ::回顾

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Adding and Subtracting Rational Expressions
::添加和减减理性表达式

Examples
::实例

Example 1
::例1

Example 2
::例2

Example 3
::例3

Example 4
::例4

Review
::回顾

Review (Answers)
::回顾(答复)