Solve 1/x(x-4)-1/(x+6)(x-4)

$$\frac { 1 } { x ( x - 4 ) } - \frac { 1 } { ( x + 6 ) ( x - 4 ) }$$

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x\left(x-4\right) and \left(x+6\right)\left(x-4\right) is x\left(x-4\right)\left(x+6\right). Multiply \frac{1}{x\left(x-4\right)} times \frac{x+6}{x+6}. Multiply \frac{1}{\left(x+6\right)\left(x-4\right)} times \frac{x}{x}.

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

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

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

Combine like terms in x+6-x.

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

Expand x\left(x-4\right)\left(x+6\right).

$$\frac{6}{x^{3}+2x^{2}-24x}$$

Expand

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x\left(x-4\right) and \left(x+6\right)\left(x-4\right) is x\left(x-4\right)\left(x+6\right). Multiply \frac{1}{x\left(x-4\right)} times \frac{x+6}{x+6}. Multiply \frac{1}{\left(x+6\right)\left(x-4\right)} times \frac{x}{x}.

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

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

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

Combine like terms in x+6-x.

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

Expand x\left(x-4\right)\left(x+6\right).

$$\frac{6}{x^{3}+2x^{2}-24x}$$