+0

# rational expressions of polynomials

-1
58
2
+204

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

Feb 24, 2021

#1
+31204
+1

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

Feb 24, 2021
#2
+266
0

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

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

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

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

$$=5-1$$

$$=4$$

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Feb 25, 2021