Help.! One Question.! LCD Common Denominator. What is the Lcd of a^2 and a+1. I came up with a^2+1, but I Don't know if that's right.

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lemjay | High School Teacher | (Level 3) Senior Educator

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To find the LCD, factor the denominators.

For the first denominator` (a^2)` , its factor is `a*a` . While the second denominator `(a+1)` is not factorable since the two terms has no GCF.

Since they have no common factor, the LCD is the product of these two denominators.

Hence, the LCD is a^2(a+1). 

Distributing `a^2` to `a+1` , the LCD can also be express as:

`a^2(a+1)=a^2*a + a^2*1 = a^3+a^2`


`:.` LCD of  `a^2`  and  `a+1`  is  `a^2(a+1)` . Can be written too as `a^3+a^2` .