Question

What is the least common denominator for the following rational equation?x/x+2 + 1/x+4 = x-1/x^2-2x-24

Answer 1

Least Common Denominator (LCD)

We are required to find the LCD for the expression:

`(x)/(x+2)+(1)/(x+4)=(x-1)/(x^2-2x-24)`

We need to have every denominator as the product of the simplest possible expressions.

Since x+2 and x+4 are already factored, we need to factor the expression:

`x^2-2x-24=(x-6)(x+4)`

Now we have the following prime factors:

x+2, x+4, x-6 and x+4

The LCD is the product of all the prime factors:

LCD = (x+2)(x+4)(x-6)