document.write( "Question 992286: Find all real or imaginary solutions for the following equation:\r
\n" ); document.write( "\n" ); document.write( "(1/x) + 1/(x-1) = (3/2)\r
\n" ); document.write( "\n" ); document.write( "I have really been struggling with using imaginaries and fractions. Help is greatly appreciated.
\n" ); document.write( "Thank you! \n" ); document.write( "

Algebra.Com's Answer #611888 by macston(5194) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( " $\"%281%2Fx%29%2B1%2F%28x-1%29=%283%2F2%29\"$ Multiply through by x.
\n" ); document.write( ".
\n" ); document.write( " $\"1%2Bx%2F%28x-1%29=%283%2F2%29%28x%29\"$ Multiply through by (x-1)
\n" ); document.write( " $\"%28x-1%29%2Bx=%283%2F2%29%28x%29%28x-1%29\"$ Multiply each side by (2/3).
\n" ); document.write( " $\"%284%2F3%29x-%282%2F3%29=x%5E2-x\"$ Subtract (4/3)x from each side.
\n" ); document.write( " $\"%28-2%2F3%29=x%5E2-%287%2F3%29x\"$ Add 2/3 to each side
\n" ); document.write( " $\"0=x%5E2-%287%2F3%29x%2B%282%2F3%29\"$ Multiply by 3.
\n" ); document.write( " $\"0=3x%5E2-7x%2B2\"$
\n" ); document.write( " $\"0=%28x-2%29%283x-1%29\"$
\n" ); document.write( " $\"x-2=0\"$ $\"OR\"$ $\"3x-1=0\"$
\n" ); document.write( " $\"x=2\"$ $\"OR\"$ $\"3x=1\"$
\n" ); document.write( " $\"x=2\"$ $\"OR\"$ $\"x=%281%2F3%29\"$ \r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

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