Question

Please just tell me what I'm doing wrong, don't tell me the answer, i need to figure it out.

Answer 1

we have the expression

`(x)/(x^2-16)-(3)/(x-4)`

REmember that

x^2-16=(x+4)(x-4)

substitute

`(x)/((x+4)(x-4))-(3)/(x-4)`

Multiply by (x+4)/(x+4) the second term

`\begin{gathered} (x)/((x+4)(x-4))-(3)/(x-4)_{}\cdot(x+4)/(x+4) \\ \\ (x)/((x+4)(x-4))-(3x+12)/((x-4)(x+4))_{} \end{gathered}`

Adds fractions with the same denominator

`\begin{gathered} (x-3x-12)/((x+4)(x-4)) \\ \\ (-2x-12)/((x+4)(x-4)) \end{gathered}`

Factor minus

`-(2x+12)/((x+4)(x-4))`

Factor 2

`-(2(x+6))/((x+4)(x-4))`