document.write( "Question 1132643: 1/(x-1)^2+1/x-1=12 \n" ); document.write( "

Algebra.Com's Answer #749735 by ikleyn(52780) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( " See how I edited your post to make it unambigous:\r
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document.write( "              1/(x-1)^2 + 1/(x-1) = 12    <<<---=== I added parentheses !\r\n" );
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\n" ); document.write( "\n" ); document.write( "Now the equation is presented clearly, and I am ready to solve it !\r
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document.write( "Introduce new variable  z = .\r\n" );
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document.write( "Then your original equation takes the form\r\n" );
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document.write( "     = 12,    or\r\n" );
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document.write( "     = 0.\r\n" );
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document.write( "Factor left side\r\n" );
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document.write( "    (z-3)*(z+4) = 0.\r\n" );
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document.write( "The two roots for z are  z= 3  and  z= -4.\r\n" );
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document.write( "Now we have two cases to analyse separately.\r\n" );
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document.write( "    Case 1.  z= 3  ====>   = 3  ====>  x-1 =   ====>  x= .\r\n" );
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document.write( "    Case 2.  z= -4  ====>   = -4  ====>  x-1 =   ====>  x= .\r\n" );
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document.write( "ANSWER.  There are two solutions  x=   and  x= .\r\n" );
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