Solve 3/13-x/x+6

$$\frac { 3 } { 13 } - \frac { x } { x + 6 }$$

Evaluate

$$\frac{2\left(9-5x\right)}{13\left(x+6\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 13 and x+6 is 13\left(x+6\right). Multiply \frac{3}{13} times \frac{x+6}{x+6}. Multiply \frac{x}{x+6} times \frac{13}{13}.

$$\frac{3\left(x+6\right)}{13\left(x+6\right)}-\frac{13x}{13\left(x+6\right)}$$

Since \frac{3\left(x+6\right)}{13\left(x+6\right)} and \frac{13x}{13\left(x+6\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3\left(x+6\right)-13x}{13\left(x+6\right)}$$

Do the multiplications in 3\left(x+6\right)-13x.

$$\frac{3x+18-13x}{13\left(x+6\right)}$$

Combine like terms in 3x+18-13x.

$$\frac{-10x+18}{13\left(x+6\right)}$$

Expand 13\left(x+6\right).

$$\frac{-10x+18}{13x+78}$$

Factor

$$\frac{2\left(9-5x\right)}{13\left(x+6\right)}$$