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Chapter 7: Problem 26

Simplify each rational expression. If the rational expression cannot be simplified, so state. $$\frac{3 x-9}{6 x}$$

Short Answer

Expert verified
The simplified form of the rational expression \(\frac{3x - 9}{6x}\) is \(\frac{(x-3)}{2x}\).

Step by step solution

01

Factorise the Numerator

Firstly, factorise the numerator, \(3x - 9\), by taking out the common factor. The common factor in these terms is 3, so the factorised form is \(3(x - 3)\).
02

Identify Common Factors in the Numerator and Denominator

Next, identify common factors between the numerator and denominator. Here, the numerator has \(3\) and the denominator has \(6\), thus \(3\) is a common factor.
03

Simplify the Expression

Then, simplify the expression \(\frac{3(x-3)}{6x}\) by cancelling the common factor 3. This leaves us with \(\frac{(x-3)}{2x}\).

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