Solve (3/5x-20-3/2x-8)

$$( \frac { 3 } { 5 x - 20 } - \frac { 3 } { 2 x - 8 } )$$

Evaluate

$$-\frac{9}{10\left(x-4\right)}$$

Short Solution Steps

Factor 5x-20. Factor 2x-8.

$$\frac{3}{5\left(x-4\right)}-\frac{3}{2\left(x-4\right)}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 5\left(x-4\right) and 2\left(x-4\right) is 10\left(x-4\right). Multiply \frac{3}{5\left(x-4\right)} times \frac{2}{2}. Multiply \frac{3}{2\left(x-4\right)} times \frac{5}{5}.

$$\frac{3\times 2}{10\left(x-4\right)}-\frac{3\times 5}{10\left(x-4\right)}$$

Since \frac{3\times 2}{10\left(x-4\right)} and \frac{3\times 5}{10\left(x-4\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3\times 2-3\times 5}{10\left(x-4\right)}$$

Do the multiplications in 3\times 2-3\times 5.

$$\frac{6-15}{10\left(x-4\right)}$$

Do the calculations in 6-15.

$$\frac{-9}{10\left(x-4\right)}$$

Expand 10\left(x-4\right).

$$\frac{-9}{10x-40}$$

Factor

$$-\frac{9}{10\left(x-4\right)}$$