Solve 6/5-x+x/4x-20

$$\frac { 6 } { 5 - x } + \frac { x } { 4 x - 20 }$$

Evaluate

$$\frac{x-24}{4\left(x-5\right)}$$

Short Solution Steps

Factor 4x-20.

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

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

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

Since \frac{6\left(-4\right)}{4\left(x-5\right)} and \frac{x}{4\left(x-5\right)} have the same denominator, add them by adding their numerators.

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

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

$$\frac{-24+x}{4\left(x-5\right)}$$

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

$$\frac{-24+x}{4x-20}$$

Factor

$$\frac{x-24}{4\left(x-5\right)}$$