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

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

Evaluate

$$\frac{2}{a}$$

Short Solution Steps

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

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

Cancel out a-b in both numerator and denominator.

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

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

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

Factor the expressions that are not already factored.

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

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

$$\frac{2}{a}$$

Expand

$$\frac{2}{a}$$

Short Solution Steps

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

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

Cancel out a-b in both numerator and denominator.

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

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

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

Factor the expressions that are not already factored.

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

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

$$\frac{2}{a}$$