document.write( "Question 30347: 2= 3/x-1/x^2 I cant find the restrictions in this problem or the least common faction if you could get that for me then i caould do the rest. \n" ); document.write( "
Algebra.Com's Answer #17095 by sdmmadam@yahoo.com(530)\"\" \"About 
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2= (3/x)-(1/x^2) ----(1)
\n" ); document.write( "Multiply by x^2 through out
\n" ); document.write( "2x^2 = 3x-1
\n" ); document.write( "2x^2-3x+1 = 0
\n" ); document.write( "2x^2-2x-x+1 = 0
\n" ); document.write( " (splitting the mid term as the sum of two terms whose product is the product of the square term and the constant term and hence -3x = (-2x)+ (-x) and (-2x)X (-x) = 2x^2 = (2x^2)X1 )
\n" ); document.write( "2x(x-1)-1(x-1) = 0
\n" ); document.write( "2xp-p= 0 (where p = (x-1) )
\n" ); document.write( "p(2x-1) = 0
\n" ); document.write( "(x-1)(2x-1) = 0
\n" ); document.write( "(x-1) = 0 gives x = 1
\n" ); document.write( "(2x-1) = 0 gives 2x = 1 which implies x = 1/2
\n" ); document.write( "Answer: x = 1 and x= 1/2
\n" ); document.write( "Verification: x = 1 in (1) we get
\n" ); document.write( "RHS = 3/x - 1/x^2 = 3/1 -1/1^2 = 3-1 = 2 = LHS
\n" ); document.write( "x = 1/2 in (1) we get
\n" ); document.write( "RHS = 3/x - 1/x^2 = [3/(1/2)] -1/[(1/2)^2] = 3X2-1/(1/4) = 6-4=2= LHS
\n" ); document.write( "Therefore our values are correct. \n" ); document.write( "
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