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Chapter 0: Problem 61

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

Short Answer

Expert verified
The simplified form of the given complex rational expression is \( \frac{x+1}{3x-1} \).

Step by step solution

01

Observe the expression

First, observe the given complex rational expression \( \frac{1+\frac{1}{x}}{3-\frac{1}{x}} \) and identify the fractions in the numerator and denominator.
02

Multiply by the common factor

To get rid of the fractions, multiply both numerator and denominator by a common factor. Here, the common factor is \( x \). So, multiply the entire expression by \( x \), giving \( \frac{x(1+\frac{1}{x})}{x(3-\frac{1}{x})} \).
03

Distribute the common factor

Distribute \( x \) in both numerator and denominator. That results in \( \frac{x+1}{3x-1} \).
04

Check for further simplifications

See whether any further simplifications can be rendered. No more simplifications are possible in this case.

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Most popular questions from this chapter

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