Question

SIMPLIFYING RATIONAL EXPRESSIONS Simplify the expression. $$\frac{2}{2 x}+\frac{12}{x}$$

Short answer

The simplified expression of \(\frac{2}{2 x}+\frac{12}{x}\) is \(\frac{13}{x}\).

Step-by-step solution

Simplify the Fractions

Before adding the fractions, it’s necessary to simplify them individually. The first fraction simplifies to \(\frac{1}{x}\), since dividing 2 by 2 leaves us with 1. The second fraction remains \(\frac{12}{x}\) as it’s already simplified.

Find a Common Denominator

Both fractions \(\frac{1}{x}\) and \(\frac{12}{x}\) already have a common denominator, which is \(x\). Therefore, there is no need for further actions to find a common denominator.

Add the Fractions

The fractions can now be added using the rule for adding rational expressions with a common denominator, \(a/b + c/b = (a+c)/b\). Therefore, \(\frac{1}{x} + \frac{12}{x}\) simplifies to \(\frac{1+12}{x}\), which is \(\frac{13}{x}\).