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

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Answer 1 · 2016-06-12T00:32:45

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!