Perform the following operation and express in simplest form. (x^(2)+3x)/(x^(2)-5x-24)÷(4x+32)/(x^(2)-64) Answer:

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Perform the following operation and express in simplest form.  (x^(2)+3x)/(x^(2)-5x-24)÷(4x+32)/(x^(2)-64) Answer:

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Factor Denominators and Numerator: First, we need to factor the denominators and the numerator of the second fraction if possible to simplify the expression. The denominator x^2 - 5x - 24 can be factored into (x - 8)(x + 3). The denominator x^2 - 64 is a difference of squares and can be factored into (x - 8)(x + 8). The numerator 4x + 32 can be factored out by 4 to get 4(x + 8).Rewrite Using Factored Forms: Now we rewrite the original expression using the factored forms: ((x^2 + 3x) / ((x - 8)(x + 3))) ÷ (4(x + 8) / ((x - 8)(x + 8))).Multiply by Reciprocal: Division of fractions is the same as multiplying by the reciprocal. So we take the reciprocal of the second fraction and multiply: ((x^2 + 3x) / ((x - 8)(x + 3))) * ((x - 8)(x + 8) / (4(x + 8))).Cancel Common Factors: We can now cancel out the common factors in the numerator and the denominator. The (x + 8) terms cancel out: ((x^2 + 3x) / ((x - 8)(x + 3))) * ((x - 8) / 4).Expand Numerator: Now we multiply the numerators and the denominators: Numerator: (x^2 + 3x) * (x - 8) Denominator: (x - 8)(x + 3) * 4Simplify Numerator and Denominator: We expand the numerator: x^2 * (x - 8) + 3x * (x - 8) = x^3 - 8x^2 + 3x^2 - 24x = x^3 - 5x^2 - 24xDivide by 4: We notice that the (x - 8) term in the numerator and the denominator will cancel out: (x^3 - 5x^2 - 24x) / (4(x + 3))Further Simplify Numerator: Now we simplify the expression by dividing each term in the numerator by 4: (x^3/4 - 5x^2/4 - 24x/4) / (x + 3)Final Simplification: Simplify the numerator further: (x^3/4 - 5x^2/4 - 6x) / (x + 3)The expression is now simplified, and we cannot simplify it further because the numerator and denominator do not have any common factors.

Perform the following operation and express in simplest form. $\newline$ $\frac{x^{2}+3 x}{x^{2}-5 x-24} \div \frac{4 x+32}{x^{2}-64}$ $\newline$ Answer:

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Perform the following operation and express in simplest form. $\newline$ $\frac{x^{2}+3 x}{x^{2}-5 x-24} \div \frac{4 x+32}{x^{2}-64}$ $\newline$ Answer: