Solve 1/x^3+1/y^3/frac{1{x}+1/y}=

$$\frac { \frac { 1 } { x ^ { 3 } } + \frac { 1 } { y ^ { 3 } } } { \frac { 1 } { x } + \frac { 1 } { y } } =$$

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x^{3} and y^{3} is x^{3}y^{3}. Multiply \frac{1}{x^{3}} times \frac{y^{3}}{y^{3}}. Multiply \frac{1}{y^{3}} times \frac{x^{3}}{x^{3}}.

$$\frac{\frac{y^{3}}{x^{3}y^{3}}+\frac{x^{3}}{x^{3}y^{3}}}{\frac{1}{x}+\frac{1}{y}}$$

Since \frac{y^{3}}{x^{3}y^{3}} and \frac{x^{3}}{x^{3}y^{3}} have the same denominator, add them by adding their numerators.

$$\frac{\frac{y^{3}+x^{3}}{x^{3}y^{3}}}{\frac{1}{x}+\frac{1}{y}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x and y is xy. Multiply \frac{1}{x} times \frac{y}{y}. Multiply \frac{1}{y} times \frac{x}{x}.

$$\frac{\frac{y^{3}+x^{3}}{x^{3}y^{3}}}{\frac{y}{xy}+\frac{x}{xy}}$$

Since \frac{y}{xy} and \frac{x}{xy} have the same denominator, add them by adding their numerators.

$$\frac{\frac{y^{3}+x^{3}}{x^{3}y^{3}}}{\frac{y+x}{xy}}$$

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

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

Cancel out xy in both numerator and denominator.

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

Factor the expressions that are not already factored.

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

Cancel out x+y in both numerator and denominator.

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

Expand

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x^{3} and y^{3} is x^{3}y^{3}. Multiply \frac{1}{x^{3}} times \frac{y^{3}}{y^{3}}. Multiply \frac{1}{y^{3}} times \frac{x^{3}}{x^{3}}.

$$\frac{\frac{y^{3}}{x^{3}y^{3}}+\frac{x^{3}}{x^{3}y^{3}}}{\frac{1}{x}+\frac{1}{y}}$$

Since \frac{y^{3}}{x^{3}y^{3}} and \frac{x^{3}}{x^{3}y^{3}} have the same denominator, add them by adding their numerators.

$$\frac{\frac{y^{3}+x^{3}}{x^{3}y^{3}}}{\frac{1}{x}+\frac{1}{y}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x and y is xy. Multiply \frac{1}{x} times \frac{y}{y}. Multiply \frac{1}{y} times \frac{x}{x}.

$$\frac{\frac{y^{3}+x^{3}}{x^{3}y^{3}}}{\frac{y}{xy}+\frac{x}{xy}}$$

Since \frac{y}{xy} and \frac{x}{xy} have the same denominator, add them by adding their numerators.

$$\frac{\frac{y^{3}+x^{3}}{x^{3}y^{3}}}{\frac{y+x}{xy}}$$

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

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

Cancel out xy in both numerator and denominator.

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

Factor the expressions that are not already factored.

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

Cancel out x+y in both numerator and denominator.

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