Solve a+a/a^2+ab*a^2b^2-a^4/ab-a

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

Evaluate

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

Short Solution Steps

Combine a and a to get 2a.

$$\frac{2a}{a^{2}+ab}\times \frac{a^{2}b^{2}-a^{4}}{ab-a}$$

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

$$\frac{2a}{a\left(a+b\right)}\times \frac{a^{2}b^{2}-a^{4}}{ab-a}$$

Cancel out a in both numerator and denominator.

$$\frac{2}{a+b}\times \frac{a^{2}b^{2}-a^{4}}{ab-a}$$

Factor the expressions that are not already factored in \frac{a^{2}b^{2}-a^{4}}{ab-a}.

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

Cancel out a in both numerator and denominator.

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

Multiply \frac{2}{a+b} times \frac{a\left(a+b\right)\left(-a+b\right)}{b-1} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out a+b in both numerator and denominator.

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

Use the distributive property to multiply 2a by -a+b.

$$\frac{-2a^{2}+2ab}{b-1}$$

Expand

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

Short Solution Steps

Combine a and a to get 2a.

$$\frac{2a}{a^{2}+ab}\times \frac{a^{2}b^{2}-a^{4}}{ab-a}$$

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

$$\frac{2a}{a\left(a+b\right)}\times \frac{a^{2}b^{2}-a^{4}}{ab-a}$$

Cancel out a in both numerator and denominator.

$$\frac{2}{a+b}\times \frac{a^{2}b^{2}-a^{4}}{ab-a}$$

Factor the expressions that are not already factored in \frac{a^{2}b^{2}-a^{4}}{ab-a}.

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

Cancel out a in both numerator and denominator.

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

Multiply \frac{2}{a+b} times \frac{a\left(a+b\right)\left(-a+b\right)}{b-1} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out a+b in both numerator and denominator.

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

Use the distributive property to multiply 2a by -a+b.

$$\frac{-2a^{2}+2ab}{b-1}$$