Solve 3/x-4-24/x^2-16

$$\frac{ 3 }{ x-4 } - \frac{ 24 }{ { x }^{ 2 } -16 }$$

Evaluate

$$\frac{3}{x+4}$$

Short Solution Steps

Factor x^{2}-16.

$$\frac{3}{x-4}-\frac{24}{\left(x-4\right)\left(x+4\right)}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-4 and \left(x-4\right)\left(x+4\right) is \left(x-4\right)\left(x+4\right). Multiply \frac{3}{x-4} times \frac{x+4}{x+4}.

$$\frac{3\left(x+4\right)}{\left(x-4\right)\left(x+4\right)}-\frac{24}{\left(x-4\right)\left(x+4\right)}$$

Since \frac{3\left(x+4\right)}{\left(x-4\right)\left(x+4\right)} and \frac{24}{\left(x-4\right)\left(x+4\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3\left(x+4\right)-24}{\left(x-4\right)\left(x+4\right)}$$

Do the multiplications in 3\left(x+4\right)-24.

$$\frac{3x+12-24}{\left(x-4\right)\left(x+4\right)}$$

Combine like terms in 3x+12-24.

$$\frac{3x-12}{\left(x-4\right)\left(x+4\right)}$$

Factor the expressions that are not already factored in \frac{3x-12}{\left(x-4\right)\left(x+4\right)}.

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

Cancel out x-4 in both numerator and denominator.

$$\frac{3}{x+4}$$

Factor

$$\frac{3}{x+4}$$