Question

Reducing the expression $\frac{a^2-b^2}{ab}-\frac{ab-b^2}{ab-a^2}$ to lowest terms, we get _______.

• A. $\frac{a}{b}$
• B. $\frac{a^2-2b^2}{ab}$
• C. $a^2$
• D. $a-2b$

Answer 1

The correct option is A $\frac{a}{b}$

We need to reduce this to lowest term : $\frac{a^2-b^2}{ab}-\frac{ab-b^2}{ab-a^2}$

It can be written as $\frac{a^2-b^2}{ab}-\frac{b(a-b)}{a(b-a)}$

$=\frac{a^2-b^2}{ab}+\frac{b}{a}$

$=\frac{a^2-b^2}{ab}+\frac{b^2}{ab}$

$=\frac{a^2}{ab}$

$=\frac{a}{b}$