Question

question 5

1. what is the lcd of the following rational equation:

\\(\frac{a}{a^2 - 36} + \frac{2}{a - 6} = \frac{1}{a + 6}\\)

a) a - 6

b) a + 6

c) (a + 6)(a - 6)

d) (a + 6)^2

Explanation:

Step1: Factor Denominators

First, factor \(a^2 - 36\) using difference of squares: \(a^2 - 36=(a + 6)(a - 6)\). The other denominators are \(a - 6\) and \(a + 6\).

Step2: Identify LCD

The LCD (Least Common Denominator) is the product of the highest power of each distinct factor. The factors are \(a + 6\) and \(a - 6\), each to the first power. So LCD is \((a + 6)(a - 6)\).

Answer:

C. \((a + 6)(a - 6)\)