Solve frac{a^{4}+a^{3}b}{a^{2}b-ab^{2}}*frac{a^{3}b-a^{2}b^{2}}{a^{2}b^2+ab^3}*b^2/a^4

$$\frac { a ^ { 4 } + a ^ { 3 } b } { a ^ { 2 } b - a b ^ { 2 } } \cdot \frac { a ^ { 3 } b - a ^ { 2 } b ^ { 2 } } { a ^ { 2 } b ^ { 2 } + a b ^ { 3 } } \cdot \frac { b ^ { 2 } } { a ^ { 4 } }$$

Evaluate

$$\frac{1}{a}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{a^{4}+a^{3}b}{a^{2}b-ab^{2}}.

$$\frac{\left(a+b\right)a^{3}}{ab\left(a-b\right)}\times \frac{a^{3}b-a^{2}b^{2}}{a^{2}b^{2}+ab^{3}}\times \frac{b^{2}}{a^{4}}$$

Cancel out a in both numerator and denominator.

$$\frac{\left(a+b\right)a^{2}}{b\left(a-b\right)}\times \frac{a^{3}b-a^{2}b^{2}}{a^{2}b^{2}+ab^{3}}\times \frac{b^{2}}{a^{4}}$$

Factor the expressions that are not already factored in \frac{a^{3}b-a^{2}b^{2}}{a^{2}b^{2}+ab^{3}}.

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

Cancel out ab in both numerator and denominator.

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

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

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

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

$$\frac{aa^{2}}{bb}\times \frac{b^{2}}{a^{4}}$$

Multiply \frac{aa^{2}}{bb} times \frac{b^{2}}{a^{4}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{aa^{2}b^{2}}{bba^{4}}$$

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

$$\frac{1}{a}$$

Expand

$$\frac{1}{a}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{a^{4}+a^{3}b}{a^{2}b-ab^{2}}.

$$\frac{\left(a+b\right)a^{3}}{ab\left(a-b\right)}\times \frac{a^{3}b-a^{2}b^{2}}{a^{2}b^{2}+ab^{3}}\times \frac{b^{2}}{a^{4}}$$

Cancel out a in both numerator and denominator.

$$\frac{\left(a+b\right)a^{2}}{b\left(a-b\right)}\times \frac{a^{3}b-a^{2}b^{2}}{a^{2}b^{2}+ab^{3}}\times \frac{b^{2}}{a^{4}}$$

Factor the expressions that are not already factored in \frac{a^{3}b-a^{2}b^{2}}{a^{2}b^{2}+ab^{3}}.

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

Cancel out ab in both numerator and denominator.

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

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

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

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

$$\frac{aa^{2}}{bb}\times \frac{b^{2}}{a^{4}}$$

Multiply \frac{aa^{2}}{bb} times \frac{b^{2}}{a^{4}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{aa^{2}b^{2}}{bba^{4}}$$

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

$$\frac{1}{a}$$