Simplify the expression below and write your final expression. (6x^(2)-384)/(2x^(2)-36 x+160)*(x-10)/(x^(2)+12 x+32)

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Simplify the expression below and write your final expression.  (6x^(2)-384)/(2x^(2)-36 x+160)*(x-10)/(x^(2)+12 x+32)

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Factor Numerator: Factor the numerator of the first fraction (6x^2 - 384). To factor out the greatest common factor, we look for the largest number that divides both terms and any common variables. In this case, the greatest common factor is 6. 6x^2 - 384 = 6(x^2 - 64) Notice that x^2 - 64 is a difference of squares and can be factored further. x^2 - 64 = (x + 8)(x - 8) So the fully factored numerator is 6(x + 8)(x - 8).Factor Denominator: Factor the denominator of the first fraction (2x^2 - 36x + 160). We look for two numbers that multiply to 2*160 = 320 and add up to -36. These numbers are -20 and -16. So we can write the denominator as: 2x^2 - 36x + 160 = 2(x^2 - 18x + 80) Now we factor the quadratic x^2 - 18x + 80 further: x^2 - 18x + 80 = (x - 10)(x - 8) So the fully factored denominator is 2(x - 10)(x - 8).Factor Numerator: Factor the numerator of the second fraction (x - 10). This is already factored, so we leave it as is.Factor Denominator: Factor the denominator of the second fraction (x^2 + 12x + 32). We look for two numbers that multiply to 32 and add up to 12. These numbers are 4 and 8. So we can write the denominator as: x^2 + 12x + 32 = (x + 4)(x + 8)Combine and Cancel: Combine the factored forms of the numerators and denominators to rewrite the original expression. ((6(x + 8)(x - 8))/(2(x - 10)(x - 8)))*((x - 10)/((x + 4)(x + 8)))Simplify Expression: Cancel out common factors from the numerators and denominators. The (x - 8) term cancels out from the first fraction's numerator and denominator. The (x - 10) term cancels out from the second fraction's numerator and the first fraction's denominator. The (x + 8) term cancels out from the first fraction's numerator and the second fraction's denominator. After canceling, we are left with: (6/(2(x + 4)))*(1/(x + 4))Simplify the remaining expression. First, we can simplify 6/2 to 3. Then, we notice that we have (1/(x + 4)) twice in the denominator, so we can combine them: 3/(x + 4)^2

Simplify the expression below and write your final expression. $\newline$ $\frac{6 x^{2}-384}{2 x^{2}-36 x+160} \cdot \frac{x-10}{x^{2}+12 x+32}$

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Simplify the expression below and write your final expression. \newline6x2−3842x2−36x+160⋅x−10x2+12x+32 \frac{6 x^{2}-384}{2 x^{2}-36 x+160} \cdot \frac{x-10}{x^{2}+12 x+32} 2x2−36x+1606x2−384​⋅x2+12x+32x−10​

Simplify the expression below and write your final expression. $\newline$ $\frac{6 x^{2}-384}{2 x^{2}-36 x+160} \cdot \frac{x-10}{x^{2}+12 x+32}$