Solve 2x^2-16/x^2-4-x+4/x-2

$$\frac { 2 x ^ { 2 } - 16 } { x ^ { 2 } - 4 } - \frac { x + 4 } { x - 2 }$$

Evaluate

$$\frac{x^{2}-6x-24}{x^{2}-4}$$

Short Solution Steps

Factor x^{2}-4.

$$\frac{2x^{2}-16}{\left(x-2\right)\left(x+2\right)}-\frac{x+4}{x-2}$$

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{x+4}{x-2} times \frac{x+2}{x+2}.

$$\frac{2x^{2}-16}{\left(x-2\right)\left(x+2\right)}-\frac{\left(x+4\right)\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}$$

Since \frac{2x^{2}-16}{\left(x-2\right)\left(x+2\right)} and \frac{\left(x+4\right)\left(x+2\right)}{\left(x-2\right)\left(x+2\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2x^{2}-16-\left(x+4\right)\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}$$

Do the multiplications in 2x^{2}-16-\left(x+4\right)\left(x+2\right).

$$\frac{2x^{2}-16-x^{2}-2x-4x-8}{\left(x-2\right)\left(x+2\right)}$$

Combine like terms in 2x^{2}-16-x^{2}-2x-4x-8.

$$\frac{x^{2}-24-6x}{\left(x-2\right)\left(x+2\right)}$$

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

$$\frac{x^{2}-24-6x}{x^{2}-4}$$

Expand

$$\frac{x^{2}-6x-24}{x^{2}-4}$$

Short Solution Steps

Factor x^{2}-4.

$$\frac{2x^{2}-16}{\left(x-2\right)\left(x+2\right)}-\frac{x+4}{x-2}$$

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{x+4}{x-2} times \frac{x+2}{x+2}.

$$\frac{2x^{2}-16}{\left(x-2\right)\left(x+2\right)}-\frac{\left(x+4\right)\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}$$

Since \frac{2x^{2}-16}{\left(x-2\right)\left(x+2\right)} and \frac{\left(x+4\right)\left(x+2\right)}{\left(x-2\right)\left(x+2\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2x^{2}-16-\left(x+4\right)\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}$$

Do the multiplications in 2x^{2}-16-\left(x+4\right)\left(x+2\right).

$$\frac{2x^{2}-16-x^{2}-2x-4x-8}{\left(x-2\right)\left(x+2\right)}$$

Combine like terms in 2x^{2}-16-x^{2}-2x-4x-8.

$$\frac{x^{2}-24-6x}{\left(x-2\right)\left(x+2\right)}$$

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

$$\frac{x^{2}-24-6x}{x^{2}-4}$$