Solve x+24/x+1-1/2

$$\frac { x + 24 } { x + 1 } - \frac { 1 } { 2 }$$

Evaluate

$$\frac{x+47}{2\left(x+1\right)}$$

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+24}{x+1} times \frac{2}{2}. Multiply \frac{1}{2} times \frac{x+1}{x+1}.

$$\frac{2\left(x+24\right)}{2\left(x+1\right)}-\frac{x+1}{2\left(x+1\right)}$$

Since \frac{2\left(x+24\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.

$$\frac{2\left(x+24\right)-\left(x+1\right)}{2\left(x+1\right)}$$

Do the multiplications in 2\left(x+24\right)-\left(x+1\right).

$$\frac{2x+48-x-1}{2\left(x+1\right)}$$

Combine like terms in 2x+48-x-1.

$$\frac{x+47}{2\left(x+1\right)}$$

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

$$\frac{x+47}{2x+2}$$

Expand

$$\frac{x+47}{2\left(x+1\right)}$$

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+24}{x+1} times \frac{2}{2}. Multiply \frac{1}{2} times \frac{x+1}{x+1}.

$$\frac{2\left(x+24\right)}{2\left(x+1\right)}-\frac{x+1}{2\left(x+1\right)}$$

Since \frac{2\left(x+24\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.

$$\frac{2\left(x+24\right)-\left(x+1\right)}{2\left(x+1\right)}$$

Do the multiplications in 2\left(x+24\right)-\left(x+1\right).

$$\frac{2x+48-x-1}{2\left(x+1\right)}$$

Combine like terms in 2x+48-x-1.

$$\frac{x+47}{2\left(x+1\right)}$$

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

$$\frac{x+47}{2x+2}$$