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Chapter 7: Problem 39

Simplify each rational expression. If the rational expression cannot be simplified, so state. $$\frac{4 x-8}{x^{2}-4 x+4}$$

Short Answer

Expert verified
The simplified form of the rational expression \( \frac{4 x-8}{x^{2}-4 x+4} \) is \( \frac{4}{x-2} \).

Step by step solution

01

Factor the numerator and denominator

Factorise the numerator as \(4(x-2)\). For the denominator , it's a perfect square trinomial, which can be factored as \((x-2)^{2}\)
02

Cancel out common factors

Now in simplified expression \( \frac{4(x-2)}{(x-2)(x-2)} \), we have a common factor (x-2) in the numerator and the denominator. Cancel out this common factor to get \( \frac{4}{x-2} \)
03

Check for further simplifications

In the simplest form \( \frac{4}{x-2} \), no further simplification is possible as now there are no common factors left in the numerator and the denominator. Hence, the provided rational expression is fully simplified.

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