Solve (a-b)^2/a^3+a^2b*a^2/b-a

$$\frac { ( a - b ) ^ { 2 } } { a ^ { 3 } + a ^ { 2 } b } \cdot \frac { a ^ { 2 } } { b - a }$$

Evaluate

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

Short Solution Steps

Multiply \frac{\left(a-b\right)^{2}}{a^{3}+a^{2}b} times \frac{a^{2}}{b-a} by multiplying numerator times numerator and denominator times denominator.

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

Factor the expressions that are not already factored.

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

Cancel out a^{2} in both numerator and denominator.

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

Expand the expression.

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

Factor the expressions that are not already factored.

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

Cancel out a-b in both numerator and denominator.

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

Expand

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

Short Solution Steps

Multiply \frac{\left(a-b\right)^{2}}{a^{3}+a^{2}b} times \frac{a^{2}}{b-a} by multiplying numerator times numerator and denominator times denominator.

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

Factor the expressions that are not already factored.

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

Cancel out a^{2} in both numerator and denominator.

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

Expand the expression.

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

Factor the expressions that are not already factored.

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

Cancel out a-b in both numerator and denominator.

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