Problem 40

Question

Simplify each rational expression. If the rational expression cannot be simplified, so state. $$\frac{x^{2}-12 x+36}{4 x-24}$$

Step-by-Step Solution

Verified
Answer
The simplified form of the given rational expression is \(\frac{x-6}{4}\)
1Step 1: Factorize the numerator and the denominator
Factorize the numerator \(x^{2}-12x+36\) to get \((x-6)^{2}\) and the denominator \(4x-24\) to get \(4(x-6)\). The expression becomes \(\frac{(x-6)^{2}}{4(x-6)}\)
2Step 2: Simplify the fraction
Cancel out the common term \(x-6\) from the numerator and the denominator. What is left is \(\frac{x-6}{4}\)