Perform the following operation and express in simplest form. (x^(2)+11 x+24)/(x^(2)-9)÷(4x+32)/(x^(3)) Answer:

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Perform the following operation and express in simplest form.  (x^(2)+11 x+24)/(x^(2)-9)÷(4x+32)/(x^(3)) 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. The expression is (x^2 + 11x + 24)/(x^2 - 9) ÷ (4x + 32)/(x^3). Rewrite as (x^2 + 11x + 24)/(x^2 - 9) * (x^3)/(4x + 32).Factor Numerators and Denominators: Factor the numerator and denominator of the first fraction and the numerator of the second fraction. The numerator x^2 + 11x + 24 can be factored into (x + 8)(x + 3). The denominator x^2 - 9 is a difference of squares and can be factored into (x + 3)(x - 3). The numerator 4x + 32 of the second fraction can be factored out by 4 to get 4(x + 8). The expression becomes ((x + 8)(x + 3))/((x + 3)(x - 3)) * (x^3)/(4(x + 8)).Cancel Common Factors: Cancel out common factors from the numerator and denominator. The (x + 8) terms cancel out, and the (x + 3) terms cancel out. The expression simplifies to 1/(x - 3) * (x^3)/4.Multiply Remaining Expressions: Multiply the remaining expressions. Multiplying 1/(x - 3) by (x^3)/4 gives (x^3)/(4(x - 3)).Check for Further Simplification: Check for any further simplification. There are no common factors to cancel out, and the expression is already in its simplest form.

Perform the following operation and express in simplest form. $\newline$ $\frac{x^{2}+11 x+24}{x^{2}-9} \div \frac{4 x+32}{x^{3}}$ $\newline$ Answer:

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Perform the following operation and express in simplest form.\newlinex2+11x+24x2−9÷4x+32x3 \frac{x^{2}+11 x+24}{x^{2}-9} \div \frac{4 x+32}{x^{3}} x2−9x2+11x+24​÷x34x+32​\newlineAnswer:

Perform the following operation and express in simplest form. $\newline$ $\frac{x^{2}+11 x+24}{x^{2}-9} \div \frac{4 x+32}{x^{3}}$ $\newline$ Answer: