How do you simplify #(4a^2+11a+6)/(a^2+4a+4) ÷ (4a^2-5a-6)#?

Question

Eva Adamson · Accepted Answer

Factor everything to see what you can eliminate.

#4a^2 + 11a + 6 # #= 4a^2 + 8a + 3a + 6# #=4a(a + 2) + 3(a + 2)# #= (4a + 3)(a + 2)# #a^2 + 4a + 4# #=(a + 2)^2# #=(a + 2)(a + 2)# #4a^2 - 5a - 6# #=4a^2 -8a + 3a - 6# #=4a(a - 2) + 3(a - 2)# #=(4a + 3)(a - 2)# Now that everything has been factored, we can put our expression back into rational form. #((4a + 3)(a + 2))/((a + 2)(a + 2)) xx 1/((4a + 3)(a - 2))# #=(cancel(4a + 3)cancel(a + 2))/(cancel(a + 2)(a + 2)) xx 1/(cancel(4a + 3)(a - 2))# #=1/((a + 2)(a - 2))# #=1/(a^2 - 4)# Hopefully this helps!

Ethan Adkins · Answer

undefined To simplify the expression (4a^2+11a+6)/(a^2+4a+4) ÷ (4a^2-5a-6), we can first factor the numerator and denominator of the first fraction and the second fraction separately.

The numerator of the first fraction can be factored as (2a+3)(2a+2), and the denominator can be factored as (a+2)(a+2).

The second fraction can be factored as (4a+3)(a-2).

Now, we can rewrite the expression as [(2a+3)(2a+2)]/[(a+2)(a+2)] ÷ [(4a+3)(a-2)].

Next, we can simplify further by canceling out common factors in the numerator and denominator.

After canceling out the common factors, the simplified expression becomes (2a+3)/(a+2) ÷ (4a+3)(a-2).

Therefore, the simplified expression is (2a+3)/(a+2) ÷ (4a+3)(a-2).