Solve 1/3-x-1/x+1

$$\frac { 1 } { 3 } - \frac { x - 1 } { x + 1 }$$

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3 and x+1 is 3\left(x+1\right). Multiply \frac{1}{3} times \frac{x+1}{x+1}. Multiply \frac{x-1}{x+1} times \frac{3}{3}.

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

Since \frac{x+1}{3\left(x+1\right)} and \frac{3\left(x-1\right)}{3\left(x+1\right)} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in x+1-3\left(x-1\right).

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

Combine like terms in x+1-3x+3.

$$\frac{-2x+4}{3\left(x+1\right)}$$

Expand 3\left(x+1\right).

$$\frac{-2x+4}{3x+3}$$

Expand

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3 and x+1 is 3\left(x+1\right). Multiply \frac{1}{3} times \frac{x+1}{x+1}. Multiply \frac{x-1}{x+1} times \frac{3}{3}.

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

Since \frac{x+1}{3\left(x+1\right)} and \frac{3\left(x-1\right)}{3\left(x+1\right)} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in x+1-3\left(x-1\right).

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

Combine like terms in x+1-3x+3.

$$\frac{-2x+4}{3\left(x+1\right)}$$

Expand 3\left(x+1\right).

$$\frac{-2x+4}{3x+3}$$