Solve 3/x^2-64-4/5x-40

$$\frac { 3 } { x ^ { 2 } - 64 } - \frac { 4 } { 5 x - 40 }$$

Evaluate

$$-\frac{4x+17}{5\left(x^{2}-64\right)}$$

Short Solution Steps

Factor x^{2}-64. Factor 5x-40.

$$\frac{3}{\left(x-8\right)\left(x+8\right)}-\frac{4}{5\left(x-8\right)}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(x-8\right)\left(x+8\right) and 5\left(x-8\right) is 5\left(x-8\right)\left(x+8\right). Multiply \frac{3}{\left(x-8\right)\left(x+8\right)} times \frac{5}{5}. Multiply \frac{4}{5\left(x-8\right)} times \frac{x+8}{x+8}.

$$\frac{3\times 5}{5\left(x-8\right)\left(x+8\right)}-\frac{4\left(x+8\right)}{5\left(x-8\right)\left(x+8\right)}$$

Since \frac{3\times 5}{5\left(x-8\right)\left(x+8\right)} and \frac{4\left(x+8\right)}{5\left(x-8\right)\left(x+8\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3\times 5-4\left(x+8\right)}{5\left(x-8\right)\left(x+8\right)}$$

Do the multiplications in 3\times 5-4\left(x+8\right).

$$\frac{15-4x-32}{5\left(x-8\right)\left(x+8\right)}$$

Combine like terms in 15-4x-32.

$$\frac{-17-4x}{5\left(x-8\right)\left(x+8\right)}$$

Expand 5\left(x-8\right)\left(x+8\right).

$$\frac{-17-4x}{5x^{2}-320}$$

Factor

$$-\frac{4x+17}{5\left(x^{2}-64\right)}$$