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

Question

asked Sep 2, 2020 65.5k views

1 Answer

Rooney · Answer 1 · 2020-09-05T17:34:00+0000

Answer:

(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).