Solve x+1/3-x+1/x+2

$$\frac { x + 1 } { 3 } - \frac { x + 1 } { x + 2 }$$

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3 and x+2 is 3\left(x+2\right). Multiply \frac{x+1}{3} times \frac{x+2}{x+2}. Multiply \frac{x+1}{x+2} times \frac{3}{3}.

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

Since \frac{\left(x+1\right)\left(x+2\right)}{3\left(x+2\right)} and \frac{3\left(x+1\right)}{3\left(x+2\right)} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in \left(x+1\right)\left(x+2\right)-3\left(x+1\right).

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

Combine like terms in x^{2}+2x+x+2-3x-3.

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

Expand 3\left(x+2\right).

$$\frac{x^{2}-1}{3x+6}$$

Expand

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3 and x+2 is 3\left(x+2\right). Multiply \frac{x+1}{3} times \frac{x+2}{x+2}. Multiply \frac{x+1}{x+2} times \frac{3}{3}.

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

Since \frac{\left(x+1\right)\left(x+2\right)}{3\left(x+2\right)} and \frac{3\left(x+1\right)}{3\left(x+2\right)} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in \left(x+1\right)\left(x+2\right)-3\left(x+1\right).

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

Combine like terms in x^{2}+2x+x+2-3x-3.

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

Expand 3\left(x+2\right).

$$\frac{x^{2}-1}{3x+6}$$