rational expressions of polynomials

Question

-1

527

2

+206

What is the sum of the $x$-values that satisfy the equation $5=\frac{x^3-2x^2-8x}{x+2}$?

oliviapow06 Feb 24, 2021

ElectricPavlov · Answer 1 · 2021-02-24T08:42:50

x cannot = 2 ( from the denominator)

NUMERATOR factors to x ( x+2)(x-4) the (x+2) in the numerator and denominator cancel and you are left with:

x^2 - 4x = 5

x^2 - 4x - 5 = 0

(x-5)(x+1) = 0 so x = 5 or -1 sum = 4

DewdropDancer · Answer 2 · 2021-02-25T03:07:34

$5=\frac{x^3-2x^2-8x}{x+2}$

$5=x\left(x-4\right)$

$x=5,\:x=-1$

$5+\left(-1\right)$

$=5-1$

$=4$

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