Solve x/2-2x/x+1

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

Evaluate

$$\frac{x\left(x-3\right)}{2\left(x+1\right)}$$

Short Solution Steps

Express 2\times \frac{x}{x+1} as a single fraction.

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

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

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

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

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

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

$$\frac{x^{2}+x-4x}{2\left(x+1\right)}$$

Combine like terms in x^{2}+x-4x.

$$\frac{x^{2}-3x}{2\left(x+1\right)}$$

Expand 2\left(x+1\right).

$$\frac{x^{2}-3x}{2x+2}$$

Factor

$$\frac{x\left(x-3\right)}{2\left(x+1\right)}$$