Question

Simplify rational expressions, explain steps

Answer 1

Answer:

The answer to your question is:  

Step-by-step explanation:

    $\frac{x - 7 }{x^{2} - 16}  - \frac{x - 1}{16 - x^{2} }$

    $\frac{x - 7 }{x^{2} - 16} + \frac{x - 1}{x^{2} - 16}$

    $\frac{x - 7 + x - 1}{x^{2} - 16}$

    $\frac{2x - 8}{(x - 4)(x + 4)}$

    $\frac{2(x - 4)}{(x - 4)(x + 4)}$

    $\frac{2}{(x + 4)}$

Answer 2

$\bf \cfrac{x-7}{x^2-16}-\cfrac{x-1}{16-x^2}\implies \cfrac{x-7}{x^2-16}-\cfrac{x-1}{-(x^2-16)}\qquad \leftarrow \stackrel{\textit{our LCD will just be}}{-(x^2-16)} \\\\\\ \cfrac{(-1)(x-7)~~~-~~~(1)(x-1)}{-(x^2-16)}\implies \cfrac{-x+7~~~-x+1}{-(x^2-16)}\implies \cfrac{-2x+8}{16-x^2}$

.

$\bf \cfrac{8-2x}{\underset{\textit{difference of squares}}{4^2-x^2}}\implies \cfrac{2~~\begin{matrix} (4-x) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{~~\begin{matrix} (4-x) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~(4+x)}\implies \cfrac{2}{4+x}$