Solve 6x/x^2-8x+4/2x-16

$$\frac { 6 x } { x ^ { 2 } - 8 x } + \frac { 4 } { 2 x - 16 }$$

Evaluate

$$\frac{8}{x-8}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{6x}{x^{2}-8x}.

$$\frac{6x}{x\left(x-8\right)}+\frac{4}{2x-16}$$

Cancel out x in both numerator and denominator.

$$\frac{6}{x-8}+\frac{4}{2x-16}$$

Factor 2x-16.

$$\frac{6}{x-8}+\frac{4}{2\left(x-8\right)}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-8 and 2\left(x-8\right) is 2\left(x-8\right). Multiply \frac{6}{x-8} times \frac{2}{2}.

$$\frac{6\times 2}{2\left(x-8\right)}+\frac{4}{2\left(x-8\right)}$$

Since \frac{6\times 2}{2\left(x-8\right)} and \frac{4}{2\left(x-8\right)} have the same denominator, add them by adding their numerators.

$$\frac{6\times 2+4}{2\left(x-8\right)}$$

Do the multiplications in 6\times 2+4.

$$\frac{12+4}{2\left(x-8\right)}$$

Do the calculations in 12+4.

$$\frac{16}{2\left(x-8\right)}$$

Expand 2\left(x-8\right).

$$\frac{16}{2x-16}$$

Factor

$$\frac{8}{x-8}$$