Perform the following operation and express in simplest form. (6x+12)/(x^(2)+11 x+18)÷(x+4)/(x^(2)+6x-27) Answer:

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Perform the following operation and express in simplest form.  (6x+12)/(x^(2)+11 x+18)÷(x+4)/(x^(2)+6x-27) Answer:

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Identify and Rewrite Division: Identify the given expression and rewrite the division as multiplication by the reciprocal of the second fraction. (6x+12)/(x^2+11x+18) ÷ (x+4)/(x^2+6x-27) = (6x+12)/(x^2+11x+18) * (x^2+6x-27)/(x+4)Factor First Fraction: Factor the numerator and denominator of the first fraction. 6x+12 can be factored as 6(x+2). x^2+11x+18 can be factored as (x+9)(x+2). The first fraction becomes 6(x+2)/((x+9)(x+2)).Factor Second Fraction: Factor the numerator and denominator of the second fraction. x^2+6x-27 can be factored as (x+9)(x-3). The second fraction becomes (x+9)(x-3)/(x+4).Combine and Cancel Factors: Combine the factored forms and cancel out common factors. (6(x+2)/((x+9)(x+2))) * ((x+9)(x-3)/(x+4)) = 6(x+9)(x-3)/((x+9)(x+4)) Here, (x+2) and (x+9) cancel out from the numerator and denominator.Simplify Remaining Expression: Simplify the remaining expression. After canceling, we are left with 6(x-3)/(x+4).Check for Further Simplification: Check for any further simplification or common factors. There are no common factors left, and the expression is in its simplest form.

Perform the following operation and express in simplest form. $\newline$ $\frac{6 x+12}{x^{2}+11 x+18} \div \frac{x+4}{x^{2}+6 x-27}$ $\newline$ Answer:

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Perform the following operation and express in simplest form. $\newline$ $\frac{6 x+12}{x^{2}+11 x+18} \div \frac{x+4}{x^{2}+6 x-27}$ $\newline$ Answer: