Solve 5/x^2+5x-24-10/x^2-9

$$\frac { 5 } { x ^ { 2 } + 5 x - 24 } - \frac { 10 } { x ^ { 2 } - 9 }$$

Evaluate

$$-\frac{5\left(x+13\right)}{\left(x+8\right)\left(x^{2}-9\right)}$$

Short Solution Steps

Factor x^{2}+5x-24. Factor x^{2}-9.

$$\frac{5}{\left(x-3\right)\left(x+8\right)}-\frac{10}{\left(x-3\right)\left(x+3\right)}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(x-3\right)\left(x+8\right) and \left(x-3\right)\left(x+3\right) is \left(x-3\right)\left(x+3\right)\left(x+8\right). Multiply \frac{5}{\left(x-3\right)\left(x+8\right)} times \frac{x+3}{x+3}. Multiply \frac{10}{\left(x-3\right)\left(x+3\right)} times \frac{x+8}{x+8}.

$$\frac{5\left(x+3\right)}{\left(x-3\right)\left(x+3\right)\left(x+8\right)}-\frac{10\left(x+8\right)}{\left(x-3\right)\left(x+3\right)\left(x+8\right)}$$

Since \frac{5\left(x+3\right)}{\left(x-3\right)\left(x+3\right)\left(x+8\right)} and \frac{10\left(x+8\right)}{\left(x-3\right)\left(x+3\right)\left(x+8\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5\left(x+3\right)-10\left(x+8\right)}{\left(x-3\right)\left(x+3\right)\left(x+8\right)}$$

Do the multiplications in 5\left(x+3\right)-10\left(x+8\right).

$$\frac{5x+15-10x-80}{\left(x-3\right)\left(x+3\right)\left(x+8\right)}$$

Combine like terms in 5x+15-10x-80.

$$\frac{-5x-65}{\left(x-3\right)\left(x+3\right)\left(x+8\right)}$$

Expand \left(x-3\right)\left(x+3\right)\left(x+8\right).

$$\frac{-5x-65}{x^{3}+8x^{2}-9x-72}$$

Factor

$$-\frac{5\left(x+13\right)}{\left(x+8\right)\left(x^{2}-9\right)}$$