Solve 6x/x^2-64+x/x+8

$$\frac{ 6x }{ { x }^{ 2 } -64 } + \frac{ x }{ x+8 }$$

Evaluate

$$\frac{x\left(x-2\right)}{x^{2}-64}$$

Short Solution Steps

Factor x^{2}-64.

$$\frac{6x}{\left(x-8\right)\left(x+8\right)}+\frac{x}{x+8}$$

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 x+8 is \left(x-8\right)\left(x+8\right). Multiply \frac{x}{x+8} times \frac{x-8}{x-8}.

$$\frac{6x}{\left(x-8\right)\left(x+8\right)}+\frac{x\left(x-8\right)}{\left(x-8\right)\left(x+8\right)}$$

Since \frac{6x}{\left(x-8\right)\left(x+8\right)} and \frac{x\left(x-8\right)}{\left(x-8\right)\left(x+8\right)} have the same denominator, add them by adding their numerators.

$$\frac{6x+x\left(x-8\right)}{\left(x-8\right)\left(x+8\right)}$$

Do the multiplications in 6x+x\left(x-8\right).

$$\frac{6x+x^{2}-8x}{\left(x-8\right)\left(x+8\right)}$$

Combine like terms in 6x+x^{2}-8x.

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

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

$$\frac{-2x+x^{2}}{x^{2}-64}$$

Factor

$$\frac{x\left(x-2\right)}{x^{2}-64}$$