Question

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

Answer 1

Answer:

(a + 1)²(a + 7).

Step-by-step explanation:

The original expression:  

$\frac{a^{3}}{a^{2}+2a+1} -\frac{3}{a^{2}+8a+7}$  

Factor each denominator:

$= \frac{a^{3}}{(a+1)(a+1)} - \frac{3}{(a+1)(a+7)}$

Factor out $\frac{ 1}{a+1 }$

$= \frac{ 1}{a+1 }(\frac{a^{3}}{a+1} - \frac{3}{a+7})$

Multiply each term by the opposite denominator and add:  

$= \frac{ 1}{a+1 }[\frac{a^{3}(a+7)-3(a+1)}{(a+1)(a+7)}]$

Remove brackets:  

$= \frac{a^{3}(a+7)-3(a+1)}{(a+1)^{2}(a+7)}$

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