Perform the following operation and express in simplest form. (x^(3))/(x^(2)-4x-32)*(x^(2)-16)/(6x^(2)) Answer:

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Perform the following operation and express in simplest form.  (x^(3))/(x^(2)-4x-32)*(x^(2)-16)/(6x^(2)) Answer:

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Factor Quadratic Expressions: We need to simplify the expression by factoring and reducing common terms where possible. First, let's factor the quadratic expressions in the denominators and the numerator where possible.Factor x^2 - 4x - 32: Factor the quadratic x^2 - 4x - 32. This can be factored into (x - 8)(x + 4) because (x - 8)(x + 4) = x^2 - 8x + 4x - 32 = x^2 - 4x - 32.Factor x^2 - 16: Factor the quadratic x^2 - 16. This is a difference of squares and can be factored into (x - 4)(x + 4) because (x - 4)(x + 4) = x^2 - 4x + 4x - 16 = x^2 - 16.Rewrite with Factored Forms: Now, rewrite the original expression with the factored forms: (x^3) / ((x - 8)(x + 4)) * ((x - 4)(x + 4)) / (6x^2).Cancel Common Factors: Next, we can cancel out the common factors in the numerator and the denominator. The (x + 4) terms cancel each other out.Cancel x^2 Terms: After canceling, the expression becomes: (x^3) / (x - 8) * (x - 4) / (6x^2).Multiply Remaining Terms: Now, we can cancel x^2 from the numerator of the first fraction and the denominator of the second fraction, leaving us with: (x) / (x - 8) * (x - 4) / 6.Final Simplification: Finally, we multiply the remaining terms. Since there are no common factors left, we simply multiply the numerators and the denominators: (x * (x - 4)) / ((x - 8) * 6).Check for Common Factors: The expression simplifies to: (x^2 - 4x) / (6x - 48).We can check if there's a common factor that can be factored out from the numerator and the denominator. However, there are no common factors, so the expression is already in its simplest form.

Perform the following operation and express in simplest form. $\newline$ $\frac{x^{3}}{x^{2}-4 x-32} \cdot \frac{x^{2}-16}{6 x^{2}}$ $\newline$ Answer:

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Perform the following operation and express in simplest form. $\newline$ $\frac{x^{3}}{x^{2}-4 x-32} \cdot \frac{x^{2}-16}{6 x^{2}}$ $\newline$ Answer: