Solve x/x+y+y/x(x+y)-1/x+y

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

Evaluate

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

Short Solution Steps

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

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

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

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

Do the multiplications in xx+y.

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

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

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

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

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

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

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

Expand

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

Short Solution Steps

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

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

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

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

Do the multiplications in xx+y.

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

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

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

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

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

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

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