Question 282570: Not sure if this falls into the category of quadratics, but here's the question, if someone can check my calculations?
Problem: Find the solution set for the equation:
[4/(6x+1)]^(1/2) - x/(x-1)=0
My solution:
use sqrt (4/(6x+1)) - x/(x-1)=0
square both sides, get
4/(6x+1)-(x/(x-1)^2=0
Cross multiply to get:
4(x^2-2x+1)=x^2(6x+1)
Multiply and condense:
6x^3-3x^2+8x-4=0
Factor to:
(2x-1)(3x^2+4)=0
For 2x-1=0, get 1/2 for x
For 3x^2+4=0, no solution, since x has to be negative number, but squared only gives positive
Does this seem right?
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website!  may seem like a solution, but if you plug it back into the original equation, then you'll find a contradiction. So is NOT a solution.
So overall, there are no real solutions.
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