Question

8/(x^2-16)+3/4=1(x-4)

Answer 1

\[
\frac{8}{x^2-16}+\frac 3 4=\frac 1 {x-4}\\
\frac{8}{(x-4)(x+4)}+\frac 3 4=\frac 1 {x-4}\\


\]
Multiply the two sides by (x-4)(x+4)

Answer 2

Multiply by 4(x-4)(x+4)
\[
32 + 3(x-4)(x+4) =4( x+4)
\]
Can you finish it from here?

Answer 3

Expand both sides
\[
3 x^2-16=4 x+16\\
3 x^2-4 x-32=0\\
(x-4) (3 x+8)=0\\
x=4\\
x=-\frac 83
\]
x=4 is not acceptable/ Why?

Answer 4

its extraneous and thank you for your help

Answer 5

yw