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

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

Evaluate

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

Short Solution Steps

Factor the expressions that are not already factored in \frac{a^{2}-b^{2}}{a^{2}+2ab+b^{2}}.

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

Cancel out a+b in both numerator and denominator.

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

Multiply \frac{a-b}{a+b} times \frac{ab+b^{2}}{a^{2}-ab} by multiplying numerator times numerator and denominator times denominator.

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

Factor the expressions that are not already factored.

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

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

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

Expand

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

Short Solution Steps

Factor the expressions that are not already factored in \frac{a^{2}-b^{2}}{a^{2}+2ab+b^{2}}.

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

Cancel out a+b in both numerator and denominator.

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

Multiply \frac{a-b}{a+b} times \frac{ab+b^{2}}{a^{2}-ab} by multiplying numerator times numerator and denominator times denominator.

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

Factor the expressions that are not already factored.

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

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

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