document.write( "Question 268825: Please help me solve this equation: $\"+x%2F%28x%2B1%29-2=3%2F%28x-3%29+\"$ \n" ); document.write( "

Algebra.Com's Answer #854065 by n2(72) $\"\"$ $\"About$

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\n" ); document.write( "Please help me solve this equation: $\"x%2F%28x%2B1%29%29-2\"$ = $\"3%2F%28x-3%29\"$
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document.write( "Your starting equation is \r\n" );
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document.write( "     = .\r\n" );
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document.write( "The domain of this equation is the set of all real numbers except of x= -1 and x= 3.\r\n" );
document.write( "We will work over the domain, assuming that x =/= -1  and  x =/= 3.\r\n" );
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document.write( "Multiply both sides by LCD (x+1)*(x-3) and simplify\r\n" );
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document.write( "    x*(x-3) - 2(x+1)*(x-3)  = 3(x+1),\r\n" );
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document.write( "    x^2 - 3x - 2*(x^2 +x - 3x - 3) = 3x + 3,\r\n" );
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document.write( "    x^2 - 3x - 2x^2 - 2x + 6x + 6 = 3x + 3,\r\n" );
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document.write( "    -x^2 - 2x - 3 = 0,\r\n" );
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document.write( "    x^2 + 2x + 3 = 0,\r\n" );
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document.write( "    (x+3)*(x-1) = 0.\r\n" );
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document.write( "The solutions to this equation are the numbers -3 and 1.\r\n" );
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document.write( "They both are in the domain of the given equation,\r\n" );
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document.write( "so the solution to equation (1) are  x = -3  and  x = 1.\r\n" );
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