Solve frac{b^{2}-a^2}{a-b}*a^4/a^5-a^4b=

$$\frac { b ^ { 2 } - a ^ { 2 } } { a - b } \cdot \frac { a ^ { 4 } } { a ^ { 5 } - a ^ { 4 } b } =$$

Evaluate

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

Short Solution Steps

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

$$\frac{\left(a+b\right)\left(-a+b\right)}{a-b}\times \frac{a^{4}}{a^{5}-a^{4}b}$$

Extract the negative sign in b-a.

$$\frac{-\left(a+b\right)\left(a-b\right)}{a-b}\times \frac{a^{4}}{a^{5}-a^{4}b}$$

Cancel out a-b in both numerator and denominator.

$$-\left(a+b\right)\times \frac{a^{4}}{a^{5}-a^{4}b}$$

Expand the expression.

$$\left(-a-b\right)\times \frac{a^{4}}{a^{5}-a^{4}b}$$

Factor the expressions that are not already factored in \frac{a^{4}}{a^{5}-a^{4}b}.

$$\left(-a-b\right)\times \frac{a^{4}}{\left(a-b\right)a^{4}}$$

Cancel out a^{4} in both numerator and denominator.

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

Express \left(-a-b\right)\times \frac{1}{a-b} as a single fraction.

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

Expand

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

Short Solution Steps

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

$$\frac{\left(a+b\right)\left(-a+b\right)}{a-b}\times \frac{a^{4}}{a^{5}-a^{4}b}$$

Extract the negative sign in b-a.

$$\frac{-\left(a+b\right)\left(a-b\right)}{a-b}\times \frac{a^{4}}{a^{5}-a^{4}b}$$

Cancel out a-b in both numerator and denominator.

$$-\left(a+b\right)\times \frac{a^{4}}{a^{5}-a^{4}b}$$

Expand the expression.

$$\left(-a-b\right)\times \frac{a^{4}}{a^{5}-a^{4}b}$$

Factor the expressions that are not already factored in \frac{a^{4}}{a^{5}-a^{4}b}.

$$\left(-a-b\right)\times \frac{a^{4}}{\left(a-b\right)a^{4}}$$

Cancel out a^{4} in both numerator and denominator.

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

Express \left(-a-b\right)\times \frac{1}{a-b} as a single fraction.

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