document.write( "Question 1090261: factor (1)/(x^(2))-(1)/(x)=6 \n" ); document.write( "

Algebra.Com's Answer #704706 by ikleyn(52786) $\"\"$ $\"About$

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\n" ); document.write( "factor (1)/(x^(2))-(1)/(x)=6
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document.write( "Introduce new variable  y = .      (1)\r\n" );
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document.write( "Then your equation will take the form\r\n" );
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document.write( " = 6,    or, equivalently,\r\n" );
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document.write( " = 0.          (2)\r\n" );
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document.write( "The left side quadratic polynomial can be easily factored \r\n" );
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document.write( "(y-3)*(y+2) = 0.      (3)\r\n" );
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document.write( "It gives the roots of the equation  y = 3  and  y = -2.\r\n" );
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document.write( "Let us consider both cases.\r\n" );
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document.write( "1.  If y = 3,   then  x =  = ,  due to (1).\r\n" );
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document.write( "2.  If y = -2,  then x =  = .\r\n" );
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document.write( "Answer.  The original equation has the roots    and  .\r\n" );
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\n" ); document.write( "\n" ); document.write( "Notice. The formulation of the problem in your post is not exactly adequate.\r
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\n" ); document.write( "\n" ); document.write( "The ideally balanced formulation is THIS:\r
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document.write( "     Solve the equation  (1)/(x^(2))-(1)/(x)=6  using factoring.\r\n" );
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