Fully simplify the expression below and write your answer as a single fraction. (x-2)/(10x^(2)-60 x+80)*(x^(2)-10 x+24)/(x^(5)-9x^(4)+18x^(3)) Answer:

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Fully simplify the expression below and write your answer as a single fraction.  (x-2)/(10x^(2)-60 x+80)*(x^(2)-10 x+24)/(x^(5)-9x^(4)+18x^(3)) Answer:

Bytelearn · Accepted Answer

Factor Quadratic Polynomials: First, factor the quadratic and cubic polynomials in the numerator and denominator where possible.Factor Cubic Polynomial: Factor the quadratic polynomial in the numerator: $x^2 - 10x + 24$. This factors into $(x-4)(x-6)$ because $-4$ and $-6$ are the roots that satisfy the equation $x^2 - 10x + 24 = 0$.Rewrite with Factored Forms: Factor the quadratic polynomial in the denominator: $10x^2 - 60x + 80$. This factors into $10(x^2 - 6x + 8)$, and further into $10(x-4)(x-2)$ because $-4$ and $-2$ are the roots that satisfy the equation $x^2 - 6x + 8 = 0$.Cancel Common Factors: Factor the cubic polynomial in the denominator: $x^5 - 9x^4 + 18x^3$. This factors into $x^3(x^2 - 9x + 18)$, and further into $x^3(x-3)(x-6)$ because $-3$ and $-6$ are the roots that satisfy the equation $x^2 - 9x + 18 = 0$.Simplify Expression: Now, rewrite the original expression with the factored forms: $\frac{(x-2)}{10(x-4)(x-2)} * \frac{(x-4)(x-6)}{x^3(x-3)(x-6)}$.Cancel out the common factors in the numerator and the denominator: The $(x-2)$ terms cancel, and the $(x-4)$ and $(x-6)$ terms cancel.The simplified expression is now: $\frac{1}{10x^3(x-3)}$.

Fully simplify the expression below and write your answer as a single fraction. $\newline$ $\frac{x-2}{10 x^{2}-60 x+80} \cdot \frac{x^{2}-10 x+24}{x^{5}-9 x^{4}+18 x^{3}}$ $\newline$ Answer:

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Fully simplify the expression below and write your answer as a single fraction.\newlinex−210x2−60x+80⋅x2−10x+24x5−9x4+18x3 \frac{x-2}{10 x^{2}-60 x+80} \cdot \frac{x^{2}-10 x+24}{x^{5}-9 x^{4}+18 x^{3}} 10x2−60x+80x−2​⋅x5−9x4+18x3x2−10x+24​\newlineAnswer:

Fully simplify the expression below and write your answer as a single fraction. $\newline$ $\frac{x-2}{10 x^{2}-60 x+80} \cdot \frac{x^{2}-10 x+24}{x^{5}-9 x^{4}+18 x^{3}}$ $\newline$ Answer: