Solve 1+h/x+h-1/x/h

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

Evaluate

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

Short Solution Steps

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

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

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

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

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

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

Combine like terms in x+hx-x-h.

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

Express \frac{\frac{hx-h}{x\left(x+h\right)}}{h} as a single fraction.

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

Factor the expressions that are not already factored.

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

Cancel out h in both numerator and denominator.

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

Expand the expression.

$$\frac{x-1}{x^{2}+hx}$$

Expand

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

Short Solution Steps

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

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

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

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

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

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

Combine like terms in x+hx-x-h.

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

Express \frac{\frac{hx-h}{x\left(x+h\right)}}{h} as a single fraction.

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

Factor the expressions that are not already factored.

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

Cancel out h in both numerator and denominator.

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

Expand the expression.

$$\frac{x-1}{x^{2}+hx}$$