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

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

Evaluate

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

Short Solution Steps

Factor x^{2}-4.

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

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 x+2 is \left(x-2\right)\left(x+2\right). Multiply \frac{2x}{x+2} times \frac{x-2}{x-2}.

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

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

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

Do the multiplications in 2x^{2}-2x\left(x-2\right).

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

Combine like terms in 2x^{2}-2x^{2}+4x.

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

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

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

Factor

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