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 complex rational expression is \(\frac{x+1}{3x-1}\)
1Step 1: Multiplying Through By the Denominator
Multiply every term in the numerator and in the denominator by \(x\), in order to remove the fractions within the fraction. This leads to: \(x(1+\frac{1}{x})/x(3-\frac{1}{x})\) which will simplify to \(\frac{x+1}{3x-1}\)
2Step 2: Factoring the Denominator
The denominator \(3x-1\) cannot be factored, so the expression is already in its simplest form