Solve frac{(a^{2}-b^{2})x^{3}}{(a^{2}+b^{2})xy^{-2}}:(a+b)x^2y^2/(a^2+b^2)=

$$\frac { ( a ^ { 2 } - b ^ { 2 } ) x ^ { 3 } } { ( a ^ { 2 } + b ^ { 2 } ) x y ^ { - 2 } } : \frac { ( a + b ) x ^ { 2 } y ^ { 2 } } { ( a ^ { 2 } + b ^ { 2 } ) } =$$

Evaluate

$$a-b$$

Short Solution Steps

Divide \frac{\left(a^{2}-b^{2}\right)x^{3}}{\left(a^{2}+b^{2}\right)xy^{-2}} by \frac{\left(a+b\right)x^{2}y^{2}}{a^{2}+b^{2}} by multiplying \frac{\left(a^{2}-b^{2}\right)x^{3}}{\left(a^{2}+b^{2}\right)xy^{-2}} by the reciprocal of \frac{\left(a+b\right)x^{2}y^{2}}{a^{2}+b^{2}}.

$$\frac{\left(a^{2}-b^{2}\right)x^{3}\left(a^{2}+b^{2}\right)}{\left(a^{2}+b^{2}\right)xy^{-2}\left(a+b\right)x^{2}y^{2}}$$

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

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

Multiply y^{-2} and y^{2} to get 1.

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

Factor the expressions that are not already factored.

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

Cancel out a+b in both numerator and denominator.

$$a-b$$

Expand

$$a-b$$

Short Solution Steps

Divide \frac{\left(a^{2}-b^{2}\right)x^{3}}{\left(a^{2}+b^{2}\right)xy^{-2}} by \frac{\left(a+b\right)x^{2}y^{2}}{a^{2}+b^{2}} by multiplying \frac{\left(a^{2}-b^{2}\right)x^{3}}{\left(a^{2}+b^{2}\right)xy^{-2}} by the reciprocal of \frac{\left(a+b\right)x^{2}y^{2}}{a^{2}+b^{2}}.

$$\frac{\left(a^{2}-b^{2}\right)x^{3}\left(a^{2}+b^{2}\right)}{\left(a^{2}+b^{2}\right)xy^{-2}\left(a+b\right)x^{2}y^{2}}$$

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

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

Multiply y^{-2} and y^{2} to get 1.

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

Factor the expressions that are not already factored.

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

Cancel out a+b in both numerator and denominator.

$$a-b$$