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

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

Evaluate

$$\frac{8}{x^{2}-4}$$

Short Solution Steps

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

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(x-2\right)\left(x+2\right) and \left(x-2\right)\left(-x-2\right) is \left(x-2\right)\left(x+2\right). Multiply \frac{4}{\left(x-2\right)\left(-x-2\right)} times \frac{-1}{-1}.

$$\frac{4}{\left(x-2\right)\left(x+2\right)}-\frac{4\left(-1\right)}{\left(x-2\right)\left(x+2\right)}$$

Since \frac{4}{\left(x-2\right)\left(x+2\right)} and \frac{4\left(-1\right)}{\left(x-2\right)\left(x+2\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4-4\left(-1\right)}{\left(x-2\right)\left(x+2\right)}$$

Do the multiplications in 4-4\left(-1\right).

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

Do the calculations in 4+4.

$$\frac{8}{\left(x-2\right)\left(x+2\right)}$$

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

$$\frac{8}{x^{2}-4}$$

Factor

$$\frac{8}{x^{2}-4}$$