Problem 61

Question

Simplify each complex rational expression. $$\frac{1+\frac{1}{x}}{3-\frac{1}{x}}$$

Step-by-Step Solution

Verified
Answer
The simplified form of the complex rational expression is \( \frac{x+1}{3x-1} \)
1Step 1: Distribute the Common Denominator to Every Term
Multiply the entire expression by \(x\) to clear the fractions in the numerator and the denominator. This results in:\[\frac{x(1+\frac{1}{x})}{x(3-\frac{1}{x})} = \frac{x+1}{3x-1}\]
2Step 2: Simplification
The expression simplified in step one does not simplify any further. The answer is \( \frac{x+1}{3x-1} \)