Fully simplify the expression below and write your answer as a single fraction. (4x^(5)-28x^(4)-32x^(3))/(2x^(5)-10x^(4)-12x^(3))*(x-6)/(x^(2)-13 x+40) Answer:

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Fully simplify the expression below and write your answer as a single fraction.  (4x^(5)-28x^(4)-32x^(3))/(2x^(5)-10x^(4)-12x^(3))*(x-6)/(x^(2)-13 x+40) Answer:

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Factor Common Terms: First, factor out the common terms in the numerator and the denominator of the first fraction. The numerator can be factored by taking out 4x^3, and the denominator can be factored by taking out 2x^3.Factor Quadratic Expressions: After factoring, the expression becomes: (4x^3(x^2 - 7x - 8))/(2x^3(x^2 - 5x - 6)) Now, factor the quadratic expressions in the parentheses.Cancel Common Terms: The quadratic x^2 - 7x - 8 can be factored into (x - 8)(x + 1). The quadratic x^2 - 5x - 6 can be factored into (x - 6)(x + 1).Simplify Second Fraction: Now, the expression looks like this: (4x^3(x - 8)(x + 1))/(2x^3(x - 6)(x + 1)) Notice that (x + 1) and x^3 can be canceled out from the numerator and the denominator.Multiply Fractions: After canceling, the expression simplifies to: (4(x - 8))/(2(x - 6)) Now, let's simplify the second fraction (x - 6)/(x^2 - 13x + 40).Cancel Terms: The quadratic x^2 - 13x + 40 can be factored into (x - 5)(x - 8). So, the second fraction becomes (x - 6)/((x - 5)(x - 8)).Simplify Constant Terms: Now, multiply the simplified first fraction by the second fraction: (4(x - 8))/(2(x - 6)) * (x - 6)/((x - 5)(x - 8)) Notice that (x - 8) can be canceled out from the numerator of the first fraction and the denominator of the second fraction.Final Simplified Expression: After canceling, the expression simplifies to: (4)/(2(x - 6)) * (x - 6)/(x - 5) Now, (x - 6) can be canceled out from the numerator of the second fraction and the denominator of the first fraction.After canceling, the expression simplifies to: (4)/(2) * (1)/(x - 5) Simplify the constant terms by dividing 4 by 2, which equals 2.The final simplified expression is: 2/(x - 5) This is the fully simplified form of the original expression written as a single fraction.

Fully simplify the expression below and write your answer as a single fraction. $\newline$ $\frac{4 x^{5}-28 x^{4}-32 x^{3}}{2 x^{5}-10 x^{4}-12 x^{3}} \cdot \frac{x-6}{x^{2}-13 x+40}$ $\newline$ Answer:

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