Question

How do you evaluate `\frac { 4} { ( x - 3) ^ { 2} } - \frac { 3} { x - 3}`?

Answer 1

`-(3x-13)/((x-3)^2)`

Explanation:

Given the expression:
`color(white)("XX")4/((x-3)^2) - 3/(x-3)`
(and assuming that `x!=3` for these terms to be meaningful)

We can modify `3/(x-3)` to have the same denominator as `4/((x-3)^2)`:
`color(white)("XX")3/(x-3)xx(x-3)/(x-3)=(3x-9)/((x-3)^2)`

Therefore
`color(white)("XX")4/((x-3)^2)-3/(x-3)`

`color(white)("XXXXXXXXXXXX")=(4-(3x-9))/((x-3)^2)`

`color(white)("XXXXXXXXXXXX")=(-3x+13)/((x-3)^2)`