Please help me solve these problems: (5y)(y+4)(y-6)   x^2+6x-18/x+8   x^5-20x^3-5x^2/-5x^2      

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sciencesolve | Teacher | (Level 3) Educator Emeritus

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You need to simplify the fraction `(x^2+6x-18)/(x+8)` , hence, you need to convert the general form of numerator x^2+6x-18 into its factored form `x^2+6x-18 = (x - x_1)(x - x_2)` , where `x_1` and `x_2` are the roots of equation `x^2+6x-18 = 0` .

Using quadratic formula to find the roots `x_1,x_2` , yields:

`x_(1,2) = (-6+-sqrt(6^2 - 4*1*(-18)))/(2*1)`

`x_(1,2) = (-6+-sqrt(36 + 72))/2`

`x_(1,2) = (-6+-sqrt108)/2 => x_(1,2) = (-6+-6sqrt3)/2 `

`x_(1,2) = -3+-3sqrt3`

Hence, converting the quadratic `x^2+6x-18` to its factored form, yields:

`(x^2+6x-18)/(x+8) = ((x + 3 - 3sqrt3)(x - 3 - 3sqrt3))/(x + 8)`

Since the numerator and denominator do not share duplicate factors, the further simplification cannot be performed.

(The other 2 points of the problem: a) `(5y)(y+4)(y-6)` , c)`(x^5-20x^3-5x^2)/(-5x^2)` , please, integrate them into separate questions)

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