Solve x/2x+8-5x+1/x+4

$$\frac { x } { 2 x + 8 } - \frac { 5 x + 1 } { x + 4 }$$

Evaluate

$$-\frac{9x+2}{2\left(x+4\right)}$$

Short Solution Steps

Factor 2x+8.

$$\frac{x}{2\left(x+4\right)}-\frac{5x+1}{x+4}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2\left(x+4\right) and x+4 is 2\left(x+4\right). Multiply \frac{5x+1}{x+4} times \frac{2}{2}.

$$\frac{x}{2\left(x+4\right)}-\frac{2\left(5x+1\right)}{2\left(x+4\right)}$$

Since \frac{x}{2\left(x+4\right)} and \frac{2\left(5x+1\right)}{2\left(x+4\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{x-2\left(5x+1\right)}{2\left(x+4\right)}$$

Do the multiplications in x-2\left(5x+1\right).

$$\frac{x-10x-2}{2\left(x+4\right)}$$

Combine like terms in x-10x-2.

$$\frac{-9x-2}{2\left(x+4\right)}$$

Expand 2\left(x+4\right).

$$\frac{-9x-2}{2x+8}$$

Expand

$$-\frac{9x+2}{2\left(x+4\right)}$$

Short Solution Steps

Factor 2x+8.

$$\frac{x}{2\left(x+4\right)}-\frac{5x+1}{x+4}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2\left(x+4\right) and x+4 is 2\left(x+4\right). Multiply \frac{5x+1}{x+4} times \frac{2}{2}.

$$\frac{x}{2\left(x+4\right)}-\frac{2\left(5x+1\right)}{2\left(x+4\right)}$$

Since \frac{x}{2\left(x+4\right)} and \frac{2\left(5x+1\right)}{2\left(x+4\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{x-2\left(5x+1\right)}{2\left(x+4\right)}$$

Do the multiplications in x-2\left(5x+1\right).

$$\frac{x-10x-2}{2\left(x+4\right)}$$

Combine like terms in x-10x-2.

$$\frac{-9x-2}{2\left(x+4\right)}$$

Expand 2\left(x+4\right).

$$\frac{-9x-2}{2x+8}$$