Solve y+1/x+1-y/x

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

Evaluate

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

Short Solution Steps

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

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

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

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

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

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

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

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

Expand x\left(x+1\right).

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

Expand

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

Short Solution Steps

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

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

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

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

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

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

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

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

Expand x\left(x+1\right).

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