Solve frac{a^{4}-b^{4}}{a^2+b^2-2ab}:a^2+ab/a-b:(a+b^2/a)

$$\frac { a ^ { 4 } - b ^ { 4 } } { a ^ { 2 } + b ^ { 2 } - 2 a b } : \frac { a ^ { 2 } + a b } { a - b } : ( a + \frac { b ^ { 2 } } { a } )$$

Evaluate

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Short Solution Steps

Divide \frac{a^{4}-b^{4}}{a^{2}+b^{2}-2ab} by \frac{a^{2}+ab}{a-b} by multiplying \frac{a^{4}-b^{4}}{a^{2}+b^{2}-2ab} by the reciprocal of \frac{a^{2}+ab}{a-b}.

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

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

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

Cancel out \left(a+b\right)\left(a-b\right)^{2} in both numerator and denominator.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply a times \frac{a}{a}.

$$\frac{\frac{a^{2}+b^{2}}{a}}{\frac{aa}{a}+\frac{b^{2}}{a}}$$

Since \frac{aa}{a} and \frac{b^{2}}{a} have the same denominator, add them by adding their numerators.

$$\frac{\frac{a^{2}+b^{2}}{a}}{\frac{aa+b^{2}}{a}}$$

Do the multiplications in aa+b^{2}.

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

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

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

Cancel out a\left(a^{2}+b^{2}\right) in both numerator and denominator.

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Factor

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