Solve 4/x+4/x-6

$$\frac { 4 } { x } + \frac { 4 } { x - 6 }$$

Evaluate

$$\frac{8\left(x-3\right)}{x\left(x-6\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x and x-6 is x\left(x-6\right). Multiply \frac{4}{x} times \frac{x-6}{x-6}. Multiply \frac{4}{x-6} times \frac{x}{x}.

$$\frac{4\left(x-6\right)}{x\left(x-6\right)}+\frac{4x}{x\left(x-6\right)}$$

Since \frac{4\left(x-6\right)}{x\left(x-6\right)} and \frac{4x}{x\left(x-6\right)} have the same denominator, add them by adding their numerators.

$$\frac{4\left(x-6\right)+4x}{x\left(x-6\right)}$$

Do the multiplications in 4\left(x-6\right)+4x.

$$\frac{4x-24+4x}{x\left(x-6\right)}$$

Combine like terms in 4x-24+4x.

$$\frac{8x-24}{x\left(x-6\right)}$$

Expand x\left(x-6\right).

$$\frac{8x-24}{x^{2}-6x}$$

Factor

$$\frac{8\left(x-3\right)}{x\left(x-6\right)}$$