Answer
$\frac{c^2}{4(b-a)}$.
Work Step by Step
The given expression is
$=\left ( \frac{a-b}{4c} \div \frac{b-a}{c} \right ) \div \frac{a-b}{c^2}$
First solve the bracket.
Replace the division sign with the multiplication sign.
$=\left ( \frac{a-b}{4c} \times \frac{c}{b-a} \right ) \div \frac{a-b}{c^2}$
We can write.
$=\left ( \frac{a-b}{4c} \times \frac{c}{-(a-b)} \right ) \div \frac{a-b}{c^2}$
Cancel common terms.
$=\left ( -\frac{1}{4} \right ) \div \frac{a-b}{c^2}$
Replace the division sign with the multiplication sign.
$=\left ( -\frac{1}{4} \right ) \times \frac{c^2}{a-b}$
Simplify.
$=\frac{c^2}{-4(a-b)}$
$=\frac{c^2}{4(b-a)}$.
