Solve 3x/x-6+6x/4x-24

$$\frac { 3 x } { x - 6 } + \frac { 6 x } { 4 x - 24 }$$

Evaluate

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

Short Solution Steps

Factor the expressions that are not already factored in \frac{6x}{4x-24}.

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

Cancel out 2 in both numerator and denominator.

$$\frac{3x}{x-6}+\frac{3x}{2\left(x-6\right)}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-6 and 2\left(x-6\right) is 2\left(x-6\right). Multiply \frac{3x}{x-6} times \frac{2}{2}.

$$\frac{2\times 3x}{2\left(x-6\right)}+\frac{3x}{2\left(x-6\right)}$$

Since \frac{2\times 3x}{2\left(x-6\right)} and \frac{3x}{2\left(x-6\right)} have the same denominator, add them by adding their numerators.

$$\frac{2\times 3x+3x}{2\left(x-6\right)}$$

Do the multiplications in 2\times 3x+3x.

$$\frac{6x+3x}{2\left(x-6\right)}$$

Combine like terms in 6x+3x.

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

Expand 2\left(x-6\right).

$$\frac{9x}{2x-12}$$

Factor

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