Solve x^2+xy/5x^2-5y^2/frac{x^2-xy{3{x}^3+3{y}^3}}

$$\frac{ \frac{ { x }^{ 2 } +xy }{ 5 { x }^{ 2 } -5 { y }^{ 2 } } }{ \frac{ { x }^{ 2 } -xy }{ 3 { x }^{ 3 } +3 { y }^{ 3 } } }$$

Evaluate

$$\frac{3\left(x^{3}+y^{3}\right)}{5\left(x-y\right)^{2}}$$

Short Solution Steps

Divide \frac{x^{2}+xy}{5x^{2}-5y^{2}} by \frac{x^{2}-xy}{3x^{3}+3y^{3}} by multiplying \frac{x^{2}+xy}{5x^{2}-5y^{2}} by the reciprocal of \frac{x^{2}-xy}{3x^{3}+3y^{3}}.

$$\frac{\left(x^{2}+xy\right)\left(3x^{3}+3y^{3}\right)}{\left(5x^{2}-5y^{2}\right)\left(x^{2}-xy\right)}$$

Factor the expressions that are not already factored.

$$\frac{3x\left(x+y\right)^{2}\left(x^{2}-xy+y^{2}\right)}{5x\left(x+y\right)\left(x-y\right)^{2}}$$

Cancel out x\left(x+y\right) in both numerator and denominator.

$$\frac{3\left(x+y\right)\left(x^{2}-xy+y^{2}\right)}{5\left(x-y\right)^{2}}$$

Expand the expression.

$$\frac{3x^{3}+3y^{3}}{5x^{2}-10xy+5y^{2}}$$

Expand

$$\frac{3\left(x^{3}+y^{3}\right)}{5\left(x-y\right)^{2}}$$

Short Solution Steps

Divide \frac{x^{2}+xy}{5x^{2}-5y^{2}} by \frac{x^{2}-xy}{3x^{3}+3y^{3}} by multiplying \frac{x^{2}+xy}{5x^{2}-5y^{2}} by the reciprocal of \frac{x^{2}-xy}{3x^{3}+3y^{3}}.

$$\frac{\left(x^{2}+xy\right)\left(3x^{3}+3y^{3}\right)}{\left(5x^{2}-5y^{2}\right)\left(x^{2}-xy\right)}$$

Factor the expressions that are not already factored.

$$\frac{3x\left(x+y\right)^{2}\left(x^{2}-xy+y^{2}\right)}{5x\left(x+y\right)\left(x-y\right)^{2}}$$

Cancel out x\left(x+y\right) in both numerator and denominator.

$$\frac{3\left(x+y\right)\left(x^{2}-xy+y^{2}\right)}{5\left(x-y\right)^{2}}$$

Expand the expression.

$$\frac{3x^{3}+3y^{3}}{5x^{2}-10xy+5y^{2}}$$