Solve frac{a^{2}+au+av+uv}{a^3+u^3}*a^2-au+u^2/a+v

$$\frac { a ^ { 2 } + a u + a v + u v } { a ^ { 3 } + u ^ { 3 } } \times \frac { a ^ { 2 } - a u + u ^ { 2 } } { a + v }$$

Evaluate

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Short Solution Steps

Factor the expressions that are not already factored in \frac{a^{2}+au+av+uv}{a^{3}+u^{3}}.

$$\frac{\left(u+a\right)\left(v+a\right)}{\left(u+a\right)\left(u^{2}-au+a^{2}\right)}\times \frac{a^{2}-au+u^{2}}{a+v}$$

Cancel out u+a in both numerator and denominator.

$$\frac{v+a}{u^{2}-au+a^{2}}\times \frac{a^{2}-au+u^{2}}{a+v}$$

Multiply \frac{v+a}{u^{2}-au+a^{2}} times \frac{a^{2}-au+u^{2}}{a+v} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(v+a\right)\left(a^{2}-au+u^{2}\right)}{\left(u^{2}-au+a^{2}\right)\left(a+v\right)}$$

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

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Factor

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