Solve 4x-3/2x+16+2x-4/x+8

$$\frac { 4 x - 3 } { 2 x + 16 } + \frac { 2 x - 4 } { x + 8 }$$

Evaluate

$$\frac{8x-11}{2\left(x+8\right)}$$

Short Solution Steps

Factor 2x+16.

$$\frac{4x-3}{2\left(x+8\right)}+\frac{2x-4}{x+8}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2\left(x+8\right) and x+8 is 2\left(x+8\right). Multiply \frac{2x-4}{x+8} times \frac{2}{2}.

$$\frac{4x-3}{2\left(x+8\right)}+\frac{2\left(2x-4\right)}{2\left(x+8\right)}$$

Since \frac{4x-3}{2\left(x+8\right)} and \frac{2\left(2x-4\right)}{2\left(x+8\right)} have the same denominator, add them by adding their numerators.

$$\frac{4x-3+2\left(2x-4\right)}{2\left(x+8\right)}$$

Do the multiplications in 4x-3+2\left(2x-4\right).

$$\frac{4x-3+4x-8}{2\left(x+8\right)}$$

Combine like terms in 4x-3+4x-8.

$$\frac{8x-11}{2\left(x+8\right)}$$

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

$$\frac{8x-11}{2x+16}$$

Expand

$$\frac{8x-11}{2\left(x+8\right)}$$

Short Solution Steps

Factor 2x+16.

$$\frac{4x-3}{2\left(x+8\right)}+\frac{2x-4}{x+8}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2\left(x+8\right) and x+8 is 2\left(x+8\right). Multiply \frac{2x-4}{x+8} times \frac{2}{2}.

$$\frac{4x-3}{2\left(x+8\right)}+\frac{2\left(2x-4\right)}{2\left(x+8\right)}$$

Since \frac{4x-3}{2\left(x+8\right)} and \frac{2\left(2x-4\right)}{2\left(x+8\right)} have the same denominator, add them by adding their numerators.

$$\frac{4x-3+2\left(2x-4\right)}{2\left(x+8\right)}$$

Do the multiplications in 4x-3+2\left(2x-4\right).

$$\frac{4x-3+4x-8}{2\left(x+8\right)}$$

Combine like terms in 4x-3+4x-8.

$$\frac{8x-11}{2\left(x+8\right)}$$

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

$$\frac{8x-11}{2x+16}$$