Solve x/x^2-4-1/2x-4

$$\frac { x } { x ^ { 2 } - 4 } - \frac { 1 } { 2 x - 4 }$$

Evaluate

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

Short Solution Steps

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

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

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

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

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

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

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

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

Combine like terms in 2x-x-2.

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

Cancel out x-2 in both numerator and denominator.

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

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

$$\frac{1}{2x+4}$$

Factor

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