Question

Simplify rational expressions, explain steps

Answer 1

`\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}`

Answer 2

The answer to your question is:

Explanation:

`(x - 7 )/(x^(2) - 16)  - (x - 1)/(16 - x^(2) )`

`(x - 7 )/(x^(2) - 16) + (x - 1)/(x^(2) - 16)`

`(x - 7 + x - 1)/(x^(2) - 16)`

`(2x - 8)/((x - 4)(x + 4))`

`(2(x - 4))/((x - 4)(x + 4))`

`(2)/((x + 4))`