SOLUTION: List all real values of x such that f(x) = 0. If there are no such real x, type DNE. If there is more that one real x, give a comma separated list (i.e.: 1,2). f(x) = 19/(x -8)

Question 204465: List all real values of x such that f(x) = 0. If there are no such real x, type DNE. If there is more that one real x, give a comma separated list (i.e.: 1,2).
f(x) = 19/(x -8) + (-18)/(x + 2)
I know I'm suppose to put f(x)=0 and solve by isolating the x but there are two different xs so I'm not sure how to approach that.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
List all real values of x such that f(x) = 0. If there are no such real x, type DNE. If there is more that one real x, give a comma separated list (i.e.: 1,2).
f(x) = 19/(x -8) + (-18)/(x + 2)
----
19/(x -8) + (-18)/(x + 2) = 0
---
Multiply thru by (x-8)(x+2)
19(x+2) + -18(x-8) = 0
19x + 38 -18x + 144 = 0
x = -182
=====================
Cheers,
Stan H.
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