Solve 6/x+4-3/5

$$\frac { 6 } { x + 4 } - \frac { 3 } { 5 }$$

Evaluate

$$\frac{3\left(6-x\right)}{5\left(x+4\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x+4 and 5 is 5\left(x+4\right). Multiply \frac{6}{x+4} times \frac{5}{5}. Multiply \frac{3}{5} times \frac{x+4}{x+4}.

$$\frac{6\times 5}{5\left(x+4\right)}-\frac{3\left(x+4\right)}{5\left(x+4\right)}$$

Since \frac{6\times 5}{5\left(x+4\right)} and \frac{3\left(x+4\right)}{5\left(x+4\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{6\times 5-3\left(x+4\right)}{5\left(x+4\right)}$$

Do the multiplications in 6\times 5-3\left(x+4\right).

$$\frac{30-3x-12}{5\left(x+4\right)}$$

Combine like terms in 30-3x-12.

$$\frac{18-3x}{5\left(x+4\right)}$$

Expand 5\left(x+4\right).

$$\frac{18-3x}{5x+20}$$

Factor

$$\frac{3\left(6-x\right)}{5\left(x+4\right)}$$