Answer
$= \frac{b-a}{4c^2} $.
Work Step by Step
Solve the operation inside the brackets.
Invert the divisor and multiply.
$\frac{a-b}{4c} \div \left ( \frac{b-a}{c} \div \frac{a-b}{c^2}\right )= \frac{a-b}{4c} \div \left ( \frac{b-a}{c} \times \frac{c^2}{a-b}\right )$
We can write.
$= \frac{a-b}{4c} \div \left ( \frac{b-a}{c} \times \frac{c^2}{-(b-a)}\right )$
Cancel common terms.
$= \frac{a-b}{4c} \div \left ( -c\right )$
Invert the divisor and multiply.
$= \frac{a-b}{4c} \times \frac{1}{\left ( -c\right )}$
Simplify.
$= \frac{-(a-b)}{4c^2} $
$= \frac{b-a}{4c^2} $.
