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 #854064 by ikleyn(53712) $\"\"$ $\"About$

You can put this solution on YOUR website!
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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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\n" ); document.write( "\n" ); document.write( "        The solution in the post by @mananth is INCORRECT.\r
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\n" ); document.write( "\n" ); document.write( "        His transformations, which he performs to reduce the given equation to the factored quadratic equation,\r
\n" ); document.write( "\n" ); document.write( "        contain a lot of arithmetic errors, and his final equation is wrong.\r
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\n" ); document.write( "\n" ); document.write( "        The answer absents in his solution. So, his presentation is a compote of mathematical symbols \r
\n" ); document.write( "\n" ); document.write( "        with no mathematical sense, which may lead a reader to wrong conclusion.\r
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\n" ); document.write( "\n" ); document.write( "        Therefore, I came to bring a correct solution.\r
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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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\n" ); document.write( "\n" ); document.write( "Solved completely and correctly.\r
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\n" ); document.write( "\n" ); document.write( "Here is my general impression about the solutions by @mananth at this forum.\r
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\n" ); document.write( "\n" ); document.write( "I just learned several months ago, that @mananth systematically uses a computer code,
\n" ); document.write( "which generates files with solutions.\r
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\n" ); document.write( "\n" ); document.write( "In many cases (approximately in 10% of cases) the solutions generated by his computer code are incorrect.\r
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\n" ); document.write( "\n" ); document.write( "But @mananth never reads and never checks what his code produces, so @mananth
\n" ); document.write( "does not carry any responsibility for the quality of his solutions.\r
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\n" ); document.write( "\n" ); document.write( "Any reader should understand it - - - @mananth does not carry any responsibility for the correctness
\n" ); document.write( "of his solutions: this is his principial position.\r
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\n" ); document.write( "\n" ); document.write( "Factually, he leaves this responsibility to those tutors (like me),
\n" ); document.write( "who check every, each and all his solutions totally.\r
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