Solve 2/x+y-1/x-y):x-y(2-x)/x^{2-y^{2}}]^{3}*[frac{(x+y)^{2}-(x-y)^{2}}{(1+x)^{2}-(1-y)^2-x^2+y^2}]^2

$$\frac { 2 } { x } + \frac { y - 1 } { x - y } ) : \frac { x - y ( 2 - x ) } { x ^ { 2 } - y ^ { 2 } } ] ^ { 3 } \cdot [ \frac { ( x + y ) ^ { 2 } - ( x - y ) ^ { 2 } } { ( 1 + x ) ^ { 2 } - ( 1 - y ) ^ { 2 } - x ^ { 2 } + y ^ { 2 } } ] ^ { 2 }$$

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x and x-y is x\left(x-y\right). Multiply \frac{2}{x} times \frac{x-y}{x-y}. Multiply \frac{y-1}{x-y} times \frac{x}{x}.

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

Since \frac{2\left(x-y\right)}{x\left(x-y\right)} and \frac{\left(y-1\right)x}{x\left(x-y\right)} have the same denominator, add them by adding their numerators.

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

Do the multiplications in 2\left(x-y\right)+\left(y-1\right)x.

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

Combine like terms in 2x-2y+yx-x.

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

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

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

Expand

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x and x-y is x\left(x-y\right). Multiply \frac{2}{x} times \frac{x-y}{x-y}. Multiply \frac{y-1}{x-y} times \frac{x}{x}.

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

Since \frac{2\left(x-y\right)}{x\left(x-y\right)} and \frac{\left(y-1\right)x}{x\left(x-y\right)} have the same denominator, add them by adding their numerators.

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

Do the multiplications in 2\left(x-y\right)+\left(y-1\right)x.

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

Combine like terms in 2x-2y+yx-x.

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

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

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