Solve 3/2x-4+1/x+2=

$$\frac { 3 } { 2 x - 4 } + \frac { 1 } { x + 2 } =$$

Evaluate

$$\frac{5x+2}{2\left(x^{2}-4\right)}$$

Short Solution Steps

Factor 2x-4.

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

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

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

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

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

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

$$\frac{3x+6+2x-4}{2\left(x-2\right)\left(x+2\right)}$$

Combine like terms in 3x+6+2x-4.

$$\frac{5x+2}{2\left(x-2\right)\left(x+2\right)}$$

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

$$\frac{5x+2}{2x^{2}-8}$$

Factor

$$\frac{5x+2}{2\left(x^{2}-4\right)}$$