Solve 11/x+1/x-y

$$1 \frac { 1 } { x } + \frac { 1 } { x - y }$$

Evaluate

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

Short Solution Steps

Express 1\times \frac{1}{x} as a single fraction.

$$\frac{1}{x}+\frac{1}{x-y}$$

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{1}{x} times \frac{x-y}{x-y}. Multiply \frac{1}{x-y} times \frac{x}{x}.

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

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

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

Combine like terms in x-y+x.

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

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

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

Differentiate w.r.t. x

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