Solve f(x)=1/x-3+1/2

$$f ( x ) = \frac { 1 } { x - 3 } + \frac { 1 } { 2 }$$

Evaluate

$$\frac{x-1}{2\left(x-3\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-3 and 2 is 2\left(x-3\right). Multiply \frac{1}{x-3} times \frac{2}{2}. Multiply \frac{1}{2} times \frac{x-3}{x-3}.

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

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

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

Combine like terms in 2+x-3.

$$\frac{-1+x}{2\left(x-3\right)}$$

Expand 2\left(x-3\right).

$$\frac{-1+x}{2x-6}$$

Factor

$$\frac{x-1}{2\left(x-3\right)}$$