Solve 1/x+1/x+18-1/12

$$\frac { 1 } { x } + \frac { 1 } { x + 18 } - \frac { 1 } { 12 }$$

Evaluate

$$-\frac{\left(x-18\right)\left(x+12\right)}{12x\left(x+18\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x and x+18 is x\left(x+18\right). Multiply \frac{1}{x} times \frac{x+18}{x+18}. Multiply \frac{1}{x+18} times \frac{x}{x}.

$$\frac{x+18}{x\left(x+18\right)}+\frac{x}{x\left(x+18\right)}-\frac{1}{12}$$

Since \frac{x+18}{x\left(x+18\right)} and \frac{x}{x\left(x+18\right)} have the same denominator, add them by adding their numerators.

$$\frac{x+18+x}{x\left(x+18\right)}-\frac{1}{12}$$

Combine like terms in x+18+x.

$$\frac{2x+18}{x\left(x+18\right)}-\frac{1}{12}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x\left(x+18\right) and 12 is 12x\left(x+18\right). Multiply \frac{2x+18}{x\left(x+18\right)} times \frac{12}{12}. Multiply \frac{1}{12} times \frac{x\left(x+18\right)}{x\left(x+18\right)}.

$$\frac{12\left(2x+18\right)}{12x\left(x+18\right)}-\frac{x\left(x+18\right)}{12x\left(x+18\right)}$$

Since \frac{12\left(2x+18\right)}{12x\left(x+18\right)} and \frac{x\left(x+18\right)}{12x\left(x+18\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{12\left(2x+18\right)-x\left(x+18\right)}{12x\left(x+18\right)}$$

Do the multiplications in 12\left(2x+18\right)-x\left(x+18\right).

$$\frac{24x+216-x^{2}-18x}{12x\left(x+18\right)}$$

Combine like terms in 24x+216-x^{2}-18x.

$$\frac{6x+216-x^{2}}{12x\left(x+18\right)}$$

Expand 12x\left(x+18\right).

$$\frac{6x+216-x^{2}}{12x^{2}+216x}$$

Factor

$$-\frac{\left(x-18\right)\left(x+12\right)}{12x\left(x+18\right)}$$