What is the right choice for question 21? http://postimage.org/image/md17spw3p/

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sciencesolve | Teacher | (Level 3) Educator Emeritus

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The problem 21 requests to you to find the simplified `((x^2-16)/(3x-9))*((x^2-6x+9)/(2x^2-11x+12))` , hence, you should write the  factored form of numerators and denominators such that:

`x^2-16 = (x-4)(x+4)`

`3x-9 = 3(x - 3)`

`x^2-6x+9 = (x - 3)^2`

You need to writethe factored form of denominator `2x^2-11x+12` , hence, you should find its zeroes using quadratic formula such that:

`x_(1,2) = (11+-sqrt(121 - 96))/4 => x_(1,2) = (11+-sqrt25)/4`

`x_(1,2) = (11+-5)/4 => x_1 = 4 ; x_2 = 3/2`

`2x^2-11x+12 = (x - 4)(x - 3/2)`

Using the factored forms in the given fractions yields:

`(((x-4)(x+4))/(3(x-3)))*((x-3)^2/((x - 4)(x - 3/2)))` = `((x+4)(x-3))/(3(2x-3))` , `x!=3/2, x!=3, x!=4`

Hence, evaluating the simplified form yields `((x+4)(x-3))/(3(2x-3)), x!=3/2, x!=3, x!=4` , hence, you need to select the second answer.

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