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

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

Evaluate

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

Short Solution Steps

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

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

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

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

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

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

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

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

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

$$\frac{x^{2}+x}{2x+4}$$

Expand

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

Short Solution Steps

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

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

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

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

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

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

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

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

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

$$\frac{x^{2}+x}{2x+4}$$