Solve a^2-b^2/4a^2+12abdiva-b/a+3b

$$\frac { a ^ { 2 } - b ^ { 2 } } { 4 a ^ { 2 } + 12 a b } \div \frac { a - b } { a + 3 b }$$

Evaluate

$$\frac{a+b}{4a}$$

Short Solution Steps

Divide \frac{a^{2}-b^{2}}{4a^{2}+12ab} by \frac{a-b}{a+3b} by multiplying \frac{a^{2}-b^{2}}{4a^{2}+12ab} by the reciprocal of \frac{a-b}{a+3b}.

$$\frac{\left(a^{2}-b^{2}\right)\left(a+3b\right)}{\left(4a^{2}+12ab\right)\left(a-b\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(a+b\right)\left(a-b\right)\left(a+3b\right)}{4a\left(a-b\right)\left(a+3b\right)}$$

Cancel out \left(a-b\right)\left(a+3b\right) in both numerator and denominator.

$$\frac{a+b}{4a}$$

Expand

$$\frac{a+b}{4a}$$

Short Solution Steps

Divide \frac{a^{2}-b^{2}}{4a^{2}+12ab} by \frac{a-b}{a+3b} by multiplying \frac{a^{2}-b^{2}}{4a^{2}+12ab} by the reciprocal of \frac{a-b}{a+3b}.

$$\frac{\left(a^{2}-b^{2}\right)\left(a+3b\right)}{\left(4a^{2}+12ab\right)\left(a-b\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(a+b\right)\left(a-b\right)\left(a+3b\right)}{4a\left(a-b\right)\left(a+3b\right)}$$

Cancel out \left(a-b\right)\left(a+3b\right) in both numerator and denominator.

$$\frac{a+b}{4a}$$