Question

I need help finding the LCD for this rato expression.

Answer 1

We are given the following expressions

`(14)/(3x^2-18x-48)\; and\; (-1)/(21x^2-84)`

We are asked to find the least common denominator (LCD) for the above expressions.

First of all, we need to factor out both the denominators

`\begin{gathered} 3x^2-18x-48 \\ 3(x^2-6x-16) \\ 3(x^2-8x+2x-16) \\ 3((x^2-8x)+(2x-16)) \\ 3(x(x^{}-8)+2(x-8)) \\ 3(x^{}-8)(x+2) \end{gathered}`

Similarly, factor out the other denominator

`\begin{gathered} 21x^2-84 \\ 21(x^2-4) \\ 21((x)^2-(2)^2) \\ 21(x+2)(x-2) \end{gathered}`

So, the expressions become

`\frac{14}{3(x^{}-8)(x+2)}\; and\; (-1)/(21(x+2)(x-2))`

The least common denominator (LCD) is

`21(x-8)(x+2)(x-2)`