Solve x-y/x^{2+xy}+xy-x^2/x^2y^2-x^4

$$\frac { x - y } { x ^ { 2 } + x y } + \frac { x y - x ^ { 2 } } { x ^ { 2 } y ^ { 2 } - x ^ { 4 } }$$

Evaluate

$$\frac{x-y+1}{x\left(x+y\right)}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{xy-x^{2}}{x^{2}y^{2}-x^{4}}.

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

Cancel out x\left(-x+y\right) in both numerator and denominator.

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

Factor x^{2}+xy.

$$\frac{x-y}{x\left(x+y\right)}+\frac{1}{x\left(x+y\right)}$$

Since \frac{x-y}{x\left(x+y\right)} and \frac{1}{x\left(x+y\right)} have the same denominator, add them by adding their numerators.

$$\frac{x-y+1}{x\left(x+y\right)}$$

Expand x\left(x+y\right).

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

Expand

$$\frac{x-y+1}{x\left(x+y\right)}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{xy-x^{2}}{x^{2}y^{2}-x^{4}}.

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

Cancel out x\left(-x+y\right) in both numerator and denominator.

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

Factor x^{2}+xy.

$$\frac{x-y}{x\left(x+y\right)}+\frac{1}{x\left(x+y\right)}$$

Since \frac{x-y}{x\left(x+y\right)} and \frac{1}{x\left(x+y\right)} have the same denominator, add them by adding their numerators.

$$\frac{x-y+1}{x\left(x+y\right)}$$

Expand x\left(x+y\right).

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