Solve a+b/abdiva^2-b^2/9a^4b

$$\frac { a + b } { a b } \div \frac { a ^ { 2 } - b ^ { 2 } } { 9 a ^ { 4 } b }$$

Evaluate

$$\frac{9a^{3}}{a-b}$$

Short Solution Steps

Divide \frac{a+b}{ab} by \frac{a^{2}-b^{2}}{9a^{4}b} by multiplying \frac{a+b}{ab} by the reciprocal of \frac{a^{2}-b^{2}}{9a^{4}b}.

$$\frac{\left(a+b\right)\times 9a^{4}b}{ab\left(a^{2}-b^{2}\right)}$$

Cancel out ab in both numerator and denominator.

$$\frac{9\left(a+b\right)a^{3}}{a^{2}-b^{2}}$$

Factor the expressions that are not already factored.

$$\frac{9\left(a+b\right)a^{3}}{\left(a+b\right)\left(a-b\right)}$$

Cancel out a+b in both numerator and denominator.

$$\frac{9a^{3}}{a-b}$$

Expand

$$\frac{9a^{3}}{a-b}$$

Short Solution Steps

Divide \frac{a+b}{ab} by \frac{a^{2}-b^{2}}{9a^{4}b} by multiplying \frac{a+b}{ab} by the reciprocal of \frac{a^{2}-b^{2}}{9a^{4}b}.

$$\frac{\left(a+b\right)\times 9a^{4}b}{ab\left(a^{2}-b^{2}\right)}$$

Cancel out ab in both numerator and denominator.

$$\frac{9\left(a+b\right)a^{3}}{a^{2}-b^{2}}$$

Factor the expressions that are not already factored.

$$\frac{9\left(a+b\right)a^{3}}{\left(a+b\right)\left(a-b\right)}$$

Cancel out a+b in both numerator and denominator.

$$\frac{9a^{3}}{a-b}$$