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Chapter 0: Problem 9

Simplify each rational expression. Find all numbers that must be excluded from the domain of the simplified rational expression. $$\frac{x^{2}-12 x+36}{4 x-24}$$

Short Answer

Expert verified
The simplified form of the given rational expression is \(\frac{(x-6)}{4}\) and the value that should be excluded from the domain is 6.

Step by step solution

01

Factorize the Expression

Factorize the expressions in the numerator and the denominator. In the numerator, we have a perfect square trinomial, so \(x^{2}-12 x+36\) becomes \((x-6)^2\). In the denominator, 4x-24 can be re-written as 4(x-6).
02

Simplify the Expression

Simplify the expression by canceling out the common expressions in the numerator and the denominator. So, \(\frac{(x-6)^2}{4(x-6)}\) simplifies to \(\frac{(x-6)}{4}\), after canceling out one of the \((x-6)\) factors.
03

Find the Excluded Values

Since division by zero leads to undefined expressions, find the values of x that make the denominator zero. So, solve the equation 4(x-6) = 0, we get x = 6. This value must be excluded from the domain of the rational expression because it makes the denominator zero.

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Most popular questions from this chapter

What does it mean to factor completely?

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