Solve frac{ab-a^{2}}{b^2-a^2}diva^2/b^2+ab

$$\frac { a b - a ^ { 2 } } { b ^ { 2 } - a ^ { 2 } } \div \frac { a ^ { 2 } } { b ^ { 2 } + a b }$$

Evaluate

$$\frac{b}{a}$$

Short Solution Steps

Divide \frac{ab-a^{2}}{b^{2}-a^{2}} by \frac{a^{2}}{b^{2}+ab} by multiplying \frac{ab-a^{2}}{b^{2}-a^{2}} by the reciprocal of \frac{a^{2}}{b^{2}+ab}.

$$\frac{\left(ab-a^{2}\right)\left(b^{2}+ab\right)}{\left(b^{2}-a^{2}\right)a^{2}}$$

Factor the expressions that are not already factored.

$$\frac{ab\left(a+b\right)\left(-a+b\right)}{\left(a+b\right)\left(-a+b\right)a^{2}}$$

Cancel out a\left(a+b\right)\left(-a+b\right) in both numerator and denominator.

$$\frac{b}{a}$$

Expand

$$\frac{b}{a}$$

Short Solution Steps

Divide \frac{ab-a^{2}}{b^{2}-a^{2}} by \frac{a^{2}}{b^{2}+ab} by multiplying \frac{ab-a^{2}}{b^{2}-a^{2}} by the reciprocal of \frac{a^{2}}{b^{2}+ab}.

$$\frac{\left(ab-a^{2}\right)\left(b^{2}+ab\right)}{\left(b^{2}-a^{2}\right)a^{2}}$$

Factor the expressions that are not already factored.

$$\frac{ab\left(a+b\right)\left(-a+b\right)}{\left(a+b\right)\left(-a+b\right)a^{2}}$$

Cancel out a\left(a+b\right)\left(-a+b\right) in both numerator and denominator.

$$\frac{b}{a}$$