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

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

Evaluate

$$\frac{1}{x+y}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{x^{2}-y^{2}}{x^{3}+y^{3}}.

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

Cancel out x+y in both numerator and denominator.

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

Multiply \frac{x-y}{x^{2}-xy+y^{2}} times \frac{x+y}{x-y} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out x-y in both numerator and denominator.

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

Multiply \frac{x+y}{x^{2}-xy+y^{2}} times \frac{x^{2}-xy+y^{2}}{x^{2}+2xy+y^{2}} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out x^{2}-xy+y^{2} in both numerator and denominator.

$$\frac{x+y}{x^{2}+2xy+y^{2}}$$

Factor the expressions that are not already factored.

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

Cancel out x+y in both numerator and denominator.

$$\frac{1}{x+y}$$

Expand

$$\frac{1}{x+y}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{x^{2}-y^{2}}{x^{3}+y^{3}}.

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

Cancel out x+y in both numerator and denominator.

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

Multiply \frac{x-y}{x^{2}-xy+y^{2}} times \frac{x+y}{x-y} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out x-y in both numerator and denominator.

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

Multiply \frac{x+y}{x^{2}-xy+y^{2}} times \frac{x^{2}-xy+y^{2}}{x^{2}+2xy+y^{2}} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out x^{2}-xy+y^{2} in both numerator and denominator.

$$\frac{x+y}{x^{2}+2xy+y^{2}}$$

Factor the expressions that are not already factored.

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

Cancel out x+y in both numerator and denominator.

$$\frac{1}{x+y}$$