Solve a+b/abdiva^2-b^2/6a^3b

$$\frac { a + b } { a b } \div \frac { a ^ { 2 } - b ^ { 2 } } { 6 a ^ { 3 } b }$$

Evaluate

$$\frac{6a^{2}}{a-b}$$

Short Solution Steps

Divide \frac{a+b}{ab} by \frac{a^{2}-b^{2}}{6a^{3}b} by multiplying \frac{a+b}{ab} by the reciprocal of \frac{a^{2}-b^{2}}{6a^{3}b}.

$$\frac{\left(a+b\right)\times 6a^{3}b}{ab\left(a^{2}-b^{2}\right)}$$

Cancel out ab in both numerator and denominator.

$$\frac{6\left(a+b\right)a^{2}}{a^{2}-b^{2}}$$

Factor the expressions that are not already factored.

$$\frac{6\left(a+b\right)a^{2}}{\left(a+b\right)\left(a-b\right)}$$

Cancel out a+b in both numerator and denominator.

$$\frac{6a^{2}}{a-b}$$

Expand

$$\frac{6a^{2}}{a-b}$$

Short Solution Steps

Divide \frac{a+b}{ab} by \frac{a^{2}-b^{2}}{6a^{3}b} by multiplying \frac{a+b}{ab} by the reciprocal of \frac{a^{2}-b^{2}}{6a^{3}b}.

$$\frac{\left(a+b\right)\times 6a^{3}b}{ab\left(a^{2}-b^{2}\right)}$$

Cancel out ab in both numerator and denominator.

$$\frac{6\left(a+b\right)a^{2}}{a^{2}-b^{2}}$$

Factor the expressions that are not already factored.

$$\frac{6\left(a+b\right)a^{2}}{\left(a+b\right)\left(a-b\right)}$$

Cancel out a+b in both numerator and denominator.

$$\frac{6a^{2}}{a-b}$$