Solve (x-1/x+2)-(1/x)

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

Evaluate

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

Short Solution Steps

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

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

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

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

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

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

Combine like terms in x^{2}-x-x-2.

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

Expand x\left(x+2\right).

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

Expand

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

Short Solution Steps

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

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

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

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

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

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

Combine like terms in x^{2}-x-x-2.

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

Expand x\left(x+2\right).

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