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

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

Evaluate

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

Short Solution Steps

Divide \frac{a^{2}-b^{2}}{a^{2}+2ab} by \frac{2a^{1}-2b}{a+b} by multiplying \frac{a^{2}-b^{2}}{a^{2}+2ab} by the reciprocal of \frac{2a^{1}-2b}{a+b}.

$$\frac{\left(a^{2}-b^{2}\right)\left(a+b\right)}{\left(a^{2}+2ab\right)\left(2a^{1}-2b\right)}$$

Calculate a to the power of 1 and get a.

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

Factor the expressions that are not already factored.

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

Cancel out a-b in both numerator and denominator.

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

Expand the expression.

$$\frac{a^{2}+2ab+b^{2}}{2a^{2}+4ab}$$

Expand

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

Short Solution Steps

Divide \frac{a^{2}-b^{2}}{a^{2}+2ab} by \frac{2a^{1}-2b}{a+b} by multiplying \frac{a^{2}-b^{2}}{a^{2}+2ab} by the reciprocal of \frac{2a^{1}-2b}{a+b}.

$$\frac{\left(a^{2}-b^{2}\right)\left(a+b\right)}{\left(a^{2}+2ab\right)\left(2a^{1}-2b\right)}$$

Calculate a to the power of 1 and get a.

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

Factor the expressions that are not already factored.

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

Cancel out a-b in both numerator and denominator.

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

Expand the expression.

$$\frac{a^{2}+2ab+b^{2}}{2a^{2}+4ab}$$