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

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

Evaluate

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

Short Solution Steps

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

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

Cancel out x in both numerator and denominator.

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

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

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

Since \frac{\left(x-y\right)x}{xy} and \frac{x^{2}+y}{xy} have the same denominator, add them by adding their numerators.

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

Do the multiplications in \left(x-y\right)x+x^{2}+y.

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

Combine like terms in x^{2}-yx+x^{2}+y.

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

Expand

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

Short Solution Steps

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

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

Cancel out x in both numerator and denominator.

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

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

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

Since \frac{\left(x-y\right)x}{xy} and \frac{x^{2}+y}{xy} have the same denominator, add them by adding their numerators.

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

Do the multiplications in \left(x-y\right)x+x^{2}+y.

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

Combine like terms in x^{2}-yx+x^{2}+y.

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