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Chapter 0: Problem 8

Simplify each rational expression. Find all numbers that must be excluded from the domain of the simplified rational expression. $$\frac{4 x-8}{x^{2}-4 x+4}$$

Short Answer

Expert verified
The simplified rational expression is \(4 / (x - 2)\), and the excluded value from its domain is 2.

Step by step solution

01

Factor the Numerator and Denominator

First, factor out the numerator and denominator of the rational expression. In this case, we factor out a 4 from the numerator: \(4(x-2)\), and we see that the denominator is a perfect square trinomial: \((x-2)^2\).
02

Simplify the Rational Expression

When simplifying rational expressions, cancel out common factors that appear in both the numerator and denominator. Here, we have a common factor of \((x-2)\). We cancel out this common factor to obtain the simplified expression: \(4 / (x-2)\).
03

Find the Excluded Values

The excluded values are those that make the denominator of the simplified expression equal to zero, as dividing by zero is undefined. Solve \(x - 2 = 0\) to obtain \(x = 2\). Therefore, 2 is excluded from the domain of the simplified rational expression.

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Most popular questions from this chapter

What is a perfect square trinomial and how is it factored?

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