SOLUTION: use an analytical method to find the solution set of the rational equation: x^-1+1=12x^-2

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Question 686236: use an analytical method to find the solution set of the rational equation:
x^-1+1=12x^-2
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
find the solution set of the rational equation:
x^-1+1=12x^-2
let u=x^-1
u^2=x^-2
u+1=12u^2
12u^2-u-1=0
(4u+1)(3u-1)=0
4u+1=0
4u=-1
u=-1/4
x^-1=-1/4
1/x=-1/4
x=-4
or
3u-1=0
3u=1
u=1/3
x^-1=1/3
1/x=1/3
x=3
solutions:
x=-4
x=3