Problem 62
Question
Simplify each complex rational expression. $$\frac{8+\frac{1}{x}}{4-\frac{1}{x}}$$
Step-by-Step Solution
Verified Answer
The simplified form of the complex rational expression \(\frac{8+\frac{1}{x}}{4-\frac{1}{x}}\) is \(\frac{8x+1}{4x-1}\).
1Step 1: Write as a single fraction on top and bottom
To start, write the complex rational expression as a single fraction on the numerator and the denominator. We'll have to multiply each term by \(x\), because \(x\) is missing in the second part of the numerator and denominator. This gives us \(\frac{8x+1}{4x-1}\)
2Step 2: Change to division of fractions
The simplification becomes easiest when the expression is written in a division form. Remember that a fraction can be seen as a division. So we have \( \frac{8x+1}{4x-1} \)
3Step 3: Simplify the fraction
In this fraction, there is nothing to factor, and no common factors in the numerator and denominator. Thus, the fraction \(\frac{8x+1}{4x-1}\) is the simplified form of the starting complex fraction.
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