Simplifying $\frac{4}{2x-7}-\frac{3}{(2x-7)^2}$

Question

A homework question asks me to "perform the addition or subtraction and simplify"

$$ \begin{gather} \frac{4}{2x-7}-\frac{3}{(2x-7)^2}=4(2x-7)-3=8x-28-3=8x-31 \\ 8x=31 \\ x=\frac{31}{8} \end{gather} $$

Is my work and answer correct?

Answer 1

If you cited the text of the exercise correctly, then you don't have to find the zero places of the given expression, only simplify it.

Writing $=$ between terms which are not equal, looks very ugly in math (is a sin).

Instead, it would be only: $$\frac 4{2x-7}-\frac 3{(2x-7)^2} = \frac{8x-31}{(2x-7)^2}\,.$$

Answer 2

Yep, perfect :), first you made the denominator equal and then it's straightforward.

But is this solving for $x$ or simplifying?