Question

Least common denominator for a^3/a^2+2a+1 and -3/a^2+8a+7

Answer 1

(a + 1)²(a + 7).

Explanation:

The original expression:

`(a^(3))/(a^(2)+2a+1) -(3)/(a^(2)+8a+7)`

Factor each denominator:

`= (a^(3))/((a+1)(a+1)) - (3)/((a+1)(a+7))`

Factor out
`( 1)/(a+1 )`

`= ( 1)/(a+1 )((a^(3))/(a+1) - (3)/(a+7))`

Multiply each term by the opposite denominator and add:

`= ( 1)/(a+1 )[(a^(3)(a+7)-3(a+1))/((a+1)(a+7))]`

Remove brackets:

`= (a^(3)(a+7)-3(a+1))/((a+1)^(2)(a+7))`

The least common denominator is (a + 1)²(a + 7).