Solve 1/2/x+1/2/15-x

$$\frac { \frac { 1 } { 2 } } { x } + \frac { \frac { 1 } { 2 } } { 15 - x }$$

Evaluate

$$\frac{15}{2x\left(15-x\right)}$$

Short Solution Steps

Express \frac{\frac{1}{2}}{x} as a single fraction.

$$\frac{1}{2x}+\frac{\frac{1}{2}}{15-x}$$

Express \frac{\frac{1}{2}}{15-x} as a single fraction.

$$\frac{1}{2x}+\frac{1}{2\left(15-x\right)}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2x and 2\left(15-x\right) is 2x\left(-x+15\right). Multiply \frac{1}{2x} times \frac{-x+15}{-x+15}. Multiply \frac{1}{2\left(15-x\right)} times \frac{x}{x}.

$$\frac{-x+15}{2x\left(-x+15\right)}+\frac{x}{2x\left(-x+15\right)}$$

Since \frac{-x+15}{2x\left(-x+15\right)} and \frac{x}{2x\left(-x+15\right)} have the same denominator, add them by adding their numerators.

$$\frac{-x+15+x}{2x\left(-x+15\right)}$$

Combine like terms in -x+15+x.

$$\frac{15}{2x\left(-x+15\right)}$$

Expand 2x\left(-x+15\right).

$$\frac{15}{-2x^{2}+30x}$$

Factor

$$\frac{15}{2x\left(15-x\right)}$$