Solve (x+y)^2/xy-y^2divxy+y^2/xy-y^2*y/x-y

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

Evaluate

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

Short Solution Steps

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

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

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

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

Factor the expressions that are not already factored in \frac{\left(x+y\right)^{2}}{xy+y^{2}}.

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

Cancel out x+y in both numerator and denominator.

$$\frac{x+y}{y}\times \frac{y}{x-y}$$

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

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

Cancel out y in both numerator and denominator.

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

Expand

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

Short Solution Steps

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

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

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

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

Factor the expressions that are not already factored in \frac{\left(x+y\right)^{2}}{xy+y^{2}}.

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

Cancel out x+y in both numerator and denominator.

$$\frac{x+y}{y}\times \frac{y}{x-y}$$

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

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

Cancel out y in both numerator and denominator.

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