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Chapter 0: Problem 62

Simplify each complex rational expression. $$\frac{8+\frac{1}{x}}{4-\frac{1}{x}}$$

Short Answer

Expert verified
The simplified form of the complex rational expression \(\frac{8+\frac{1}{x}}{4-\frac{1}{x}}\) is \(\frac{8x+1}{4x-1}\).

Step by step solution

01

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 \(\frac{8x+1}{4x-1}\)
02

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 \( \frac{8x+1}{4x-1} \)
03

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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