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

Factor everything to see what you can eliminate.

Now that everything has been factored, we can put our expression back into rational form.

Hopefully this helps!

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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).

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