document.write( "Question 1054591: Solve the equation.\r
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Algebra.Com's Answer #669802 by Edwin McCravy(20060) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "You didn't put enough parentheses when you typed in your equation:\r\n" );
document.write( "It should be:\r\n" );
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document.write( "1/(x+4)=2/(x^2+3x-4)-1/(1-x) \r\n" );
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document.write( "not this 1/x+4=2/x^2+3x-4-1/1-x\r\n" );
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document.write( "You want it to mean the same as this:\r\n" );
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document.write( "Not the same as this \r\n" );
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document.write( "Before we get a common denominator we must simplify.\r\n" );
document.write( "We factor the denominator x²+3x-4 as (x+4)(x-1) and change \r\n" );
document.write( "the denominator 1-x to descending order -x+1, and then\r\n" );
document.write( "factor out a negative sign as -(x-1) by changing the \r\n" );
document.write( "sign inside the parentheses.  So now we have\r\n" );
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document.write( "or\r\n" );
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document.write( "  <--eq. #1\r\n" );
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document.write( "Now the common denominator is (x+4)(x-1).  Since it is\r\n" );
document.write( "an equation and not just an expression without an equal\r\n" );
document.write( "sign, we may multiply both sides by the LCD over 1, which\r\n" );
document.write( "I'll write as \r\n" );
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document.write( "Notice that we have multiplied that LCD by every term of \r\n" );
document.write( "eq. #1 above.\r\n" );
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document.write( "Now we can cancel and eventually we'll end up with no fractions:\r\n" );
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document.write( "And if we ignore the ones in the denominators, we have just:\r\n" );
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document.write( "or \r\n" );
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document.write( "Subtract x from both sides:\r\n" );
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document.write( "This is false, so there is no solution\r\n" );
document.write( "to the given problem, but we could not\r\n" );
document.write( "have known that it had no solution until \r\n" );
document.write( "we got to a false equation containing no \r\n" );
document.write( "variables.  Other very similar equations\r\n" );
document.write( "to this one do have solutions because the\r\n" );
document.write( "variables x's don't all cancel out as they \r\n" );
document.write( "did in this equation.\r\n" );
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document.write( "Edwin

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