document.write( "Question 282570: Not sure if this falls into the category of quadratics, but here's the question, if someone can check my calculations?
\n" ); document.write( "Problem: Find the solution set for the equation:
\n" ); document.write( "[4/(6x+1)]^(1/2) - x/(x-1)=0\r
\n" ); document.write( "\n" ); document.write( "My solution:
\n" ); document.write( "use sqrt (4/(6x+1)) - x/(x-1)=0
\n" ); document.write( "square both sides, get
\n" ); document.write( "4/(6x+1)-(x/(x-1)^2=0
\n" ); document.write( "Cross multiply to get:
\n" ); document.write( "4(x^2-2x+1)=x^2(6x+1)
\n" ); document.write( "Multiply and condense:
\n" ); document.write( "6x^3-3x^2+8x-4=0
\n" ); document.write( "Factor to:
\n" ); document.write( "(2x-1)(3x^2+4)=0
\n" ); document.write( "For 2x-1=0, get 1/2 for x
\n" ); document.write( "For 3x^2+4=0, no solution, since x has to be negative number, but squared only gives positive
\n" ); document.write( "Does this seem right? \n" ); document.write( "

Algebra.Com's Answer #205178 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"x=1%2F2\"$ may seem like a solution, but if you plug it back into the original equation, then you'll find a contradiction. So $\"x=1%2F2\"$ is NOT a solution.\r
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\n" ); document.write( "\n" ); document.write( "So overall, there are no real solutions. \n" ); document.write( "

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