Solve 1/x-4-1/(x-4)(x+2)

$$\frac { 1 } { x - 4 } - \frac { 1 } { ( x - 4 ) ( x + 2 ) }$$

Evaluate

$$\frac{x+1}{\left(x-4\right)\left(x+2\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-4 and \left(x-4\right)\left(x+2\right) is \left(x-4\right)\left(x+2\right). Multiply \frac{1}{x-4} times \frac{x+2}{x+2}.

$$\frac{x+2}{\left(x-4\right)\left(x+2\right)}-\frac{1}{\left(x-4\right)\left(x+2\right)}$$

Since \frac{x+2}{\left(x-4\right)\left(x+2\right)} and \frac{1}{\left(x-4\right)\left(x+2\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{x+2-1}{\left(x-4\right)\left(x+2\right)}$$

Combine like terms in x+2-1.

$$\frac{x+1}{\left(x-4\right)\left(x+2\right)}$$

Expand \left(x-4\right)\left(x+2\right).

$$\frac{x+1}{x^{2}-2x-8}$$

Expand

$$\frac{x+1}{\left(x-4\right)\left(x+2\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-4 and \left(x-4\right)\left(x+2\right) is \left(x-4\right)\left(x+2\right). Multiply \frac{1}{x-4} times \frac{x+2}{x+2}.

$$\frac{x+2}{\left(x-4\right)\left(x+2\right)}-\frac{1}{\left(x-4\right)\left(x+2\right)}$$

Since \frac{x+2}{\left(x-4\right)\left(x+2\right)} and \frac{1}{\left(x-4\right)\left(x+2\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{x+2-1}{\left(x-4\right)\left(x+2\right)}$$

Combine like terms in x+2-1.

$$\frac{x+1}{\left(x-4\right)\left(x+2\right)}$$

Expand \left(x-4\right)\left(x+2\right).

$$\frac{x+1}{x^{2}-2x-8}$$