Solve x^2+xy/x*y/xy+y^2-y^2y/x^2

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

Evaluate

$$-\frac{y^{3}}{x^{2}}+1$$

Short Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

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

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

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

Cancel out x in both numerator and denominator.

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

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

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

Cancel out y in both numerator and denominator.

$$\left(x+y\right)\times \frac{1}{x+y}-\frac{y^{3}}{x^{2}}$$

Cancel out x+y and x+y.

$$1-\frac{y^{3}}{x^{2}}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{x^{2}}{x^{2}}.

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

Since \frac{x^{2}}{x^{2}} and \frac{y^{3}}{x^{2}} have the same denominator, subtract them by subtracting their numerators.

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

Expand

$$-\frac{y^{3}}{x^{2}}+1$$

Short Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

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

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

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

Cancel out x in both numerator and denominator.

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

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

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

Cancel out y in both numerator and denominator.

$$\left(x+y\right)\times \frac{1}{x+y}-\frac{y^{3}}{x^{2}}$$

Cancel out x+y and x+y.

$$1-\frac{y^{3}}{x^{2}}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{x^{2}}{x^{2}}.

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

Since \frac{x^{2}}{x^{2}} and \frac{y^{3}}{x^{2}} have the same denominator, subtract them by subtracting their numerators.

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