Question

Simplify the expression. $$\frac{7}{2 x}+\frac{x+2}{2 x}$$

Short answer

The simplified form of the expression \( \frac{7}{2x} + \frac{x+2}{2x} \) is \( \frac{9+x}{2x} \).

Step-by-step solution

Identify the common denominator

Here both terms in the expression, \( \frac{7}{2x} \) and \( \frac{x+2}{2x} \), share the same denominator, 2x. So, 2x is our common denominator.

Add the fractions

Adding the two fractions \( \frac{7}{2x} \) and \( \frac{x+2}{2x} \) with the common denominator will look like this: \( \frac{7}{2x} + \frac{x+2}{2x} = \frac{7 + (x + 2)}{2x} \).

Simplify the numerator

The numerator becomes \( 7 + x + 2. \)

Solve the numerator

Solving the numerator results in \( 9 + x. \)

Writing the final expression

The final expression is \( \frac{9+x}{2x} \).