Fully simplify the expression below and write your answer as a single fraction. (10x^(2)-10 x-420)/(5x^(2)-80 x+315)*(x^(3)-14x^(2)+45 x)/(x^(4)-5x^(3)) Answer:

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Fully simplify the expression below and write your answer as a single fraction.  (10x^(2)-10 x-420)/(5x^(2)-80 x+315)*(x^(3)-14x^(2)+45 x)/(x^(4)-5x^(3)) Answer:

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Factor Numerator 1: First, let's factor each polynomial in the expression, if possible. We start with the numerator of the first fraction (10x^2 - 10x - 420). Factor out the greatest common factor, which is 10: 10(x^2 - x - 42) Now, factor the quadratic: 10(x - 7)(x + 6)Factor Denominator 1: Next, factor the denominator of the first fraction (5x^2 - 80x + 315). Factor out the greatest common factor, which is 5: 5(x^2 - 16x + 63) Now, factor the quadratic: 5(x - 7)(x - 9)Factor Numerator 2: Now, let's factor the numerator of the second fraction (x^3 - 14x^2 + 45x). Factor out the greatest common factor, which is x: x(x^2 - 14x + 45) Now, factor the quadratic: x(x - 9)(x - 5)Factor Denominator 2: Finally, factor the denominator of the second fraction (x^4 - 5x^3). Factor out the greatest common factor, which is x^3: x^3(x - 5)Rewrite with Factored Forms: Now we rewrite the original expression with the factored forms: (10(x - 7)(x + 6))/(5(x - 7)(x - 9)) * (x(x - 9)(x - 5))/(x^3(x - 5))Cancel Common Factors: Next, we cancel out the common factors in the numerators and denominators: The (x - 7) terms cancel, one (x - 9) term cancels, and one (x - 5) term cancels. Also, we can cancel one x from the numerator of the second fraction with one x from x^3 in the denominator of the second fraction. This leaves us with: (10(x + 6))/(5) * (x)/(x^2)Simplify Remaining Expression: Now, simplify the remaining expression: The 10 in the numerator and the 5 in the denominator can be simplified to 2. The x in the numerator and one of the x's in x^2 in the denominator cancel out. This leaves us with: 2(x + 6)/xWrite Simplified Expression: Finally, we write the simplified expression as a single fraction: 2(x + 6)/x

Fully simplify the expression below and write your answer as a single fraction. $\newline$ $\frac{10 x^{2}-10 x-420}{5 x^{2}-80 x+315} \cdot \frac{x^{3}-14 x^{2}+45 x}{x^{4}-5 x^{3}}$ $\newline$ Answer:

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