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

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

Evaluate

$$\frac{b}{2}+1$$

Short Solution Steps

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

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

Factor the expressions that are not already factored.

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

Extract the negative sign in 1-a. Extract the negative sign in b-a.

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

Cancel out \left(a-1\right)\left(a+b\right)\left(a-b\right) in both numerator and denominator.

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

Expand the expression.

$$\frac{b+2}{2}$$

Expand

$$\frac{b}{2}+1$$

Short Solution Steps

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

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

Factor the expressions that are not already factored.

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

Extract the negative sign in 1-a. Extract the negative sign in b-a.

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

Cancel out \left(a-1\right)\left(a+b\right)\left(a-b\right) in both numerator and denominator.

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

Expand the expression.

$$\frac{b+2}{2}$$