Solve (x-1)/x+4-1/2

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

Evaluate

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

Short Solution Steps

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

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

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

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

Do the multiplications in 2\left(x-1\right)-\left(x+4\right).

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

Combine like terms in 2x-2-x-4.

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

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

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

Expand

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

Short Solution Steps

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

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

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

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

Do the multiplications in 2\left(x-1\right)-\left(x+4\right).

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

Combine like terms in 2x-2-x-4.

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

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

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