Question

SIMPLIFYING RATIONAL EXPRESSIONS Simplify the expression. $$\frac{3}{x}+\frac{x+9}{x}$$

Short answer

The simplified form of the expression \(\frac{3}{x} + \frac{x + 9}{x}\) is \(\frac{x + 12}{x}\).

Step-by-step solution

Identify common denominator

Identify the common denominator of the two fractions. In this case, the common denominator for both fractions is \(x\).

Simplify the expression

Since the denominators are the same, the two fractions can be combined by adding the numerators: \(\frac{3}{x} + \frac{x+9}{x} = \frac{3+x+9}{x}\).

Simplify the numerator

The numerator simplifies to \(3+x+9\), which can be further simplified to \(x+12\). Therefore, \(\frac{3}{x} + \frac{x + 9}{x}\) simplifies to \(\frac{x + 12}{x}\).