Solve x+b/x-1-1/2

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

Evaluate

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

Short Solution Steps

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

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

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

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

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

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

Combine like terms in 2x+2b-x+1.

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

Expand 2\left(x-1\right).

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

Expand

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

Short Solution Steps

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

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

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

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

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

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

Combine like terms in 2x+2b-x+1.

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

Expand 2\left(x-1\right).

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