Solve 3/2x+4+2/x^2-4

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

Evaluate

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

Short Solution Steps

Factor 2x+4. Factor x^{2}-4.

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

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

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

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

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

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

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

Combine like terms in 3x-6+4.

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

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

$$\frac{3x-2}{2x^{2}-8}$$

Factor

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