document.write( "Question 37341: 
   1         1          3\r\n" );
document.write( "——————— + ——————— = —————————\r\n" );
document.write( " t - 1     t + 2     t2 + t-2\r\n" );
document.write( "Please help me figure out this problem. I think it may have no solution.
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Algebra.Com's Answer #22983 by AnlytcPhil(1807)\"\" \"About 
You can put this solution on YOUR website!
Solve for t:\r\n" );
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document.write( "   1         1          3\r\n" );
document.write( "——————— + ——————— = —————————\r\n" );
document.write( " t - 1     t + 2     t2 + t-2\r\n" );
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document.write( "My graphing calculator says it has solution t = -1.390957657, but\r\n" );
document.write( "that may be too hard to calculate by hand.  But let's try anyway:\r\n" );
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document.write( "First we need to get rid of the negative exponent on the right\r\n" );
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document.write( "            3\r\n" );
document.write( "        —————————\r\n" );
document.write( "         t2 + t-2\r\n" );
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document.write( "Multiply top and bottom by t2\r\n" );
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document.write( "          3(t2)        3t2\r\n" );
document.write( "       —————————— = —————————\r\n" );
document.write( "       (t2 + t-2)    t4 + 1\r\n" );
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document.write( "   1         1         3t2\r\n" );
document.write( "——————— + ——————— = —————————\r\n" );
document.write( " t - 1     t + 2     t4 + 1\r\n" );
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document.write( "Multiply each fraction through by the LCD = (t - 1)(t + 2)(t4 + 1)\r\n" );
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document.write( " (t + 2)(t4 + 1) + (t - 1)(t4 + 1) = 3t2(t - 1)(t + 2)\r\n" );
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document.write( " t5 + t + 2t4 + 2 + t5 + t - t4 - 1 = 3t2(t2 + t - 2)\r\n" );
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document.write( "                  2t5 + t4 + 2t + 1 = 3t4 + 3t3 - 6t2 \r\n" );
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document.write( "     2t5 - 2t4 - 3t3 + 6t2 + 2t + 1 = 0\r\n" );
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document.write( "The only rational solutions possible are ±1, ±1/2, but none of\r\n" );
document.write( "these turn out to be solutions.  So it cannot be solved by any \r\n" );
document.write( "methods of ordinary algebra.  However it DOES have one irrational\r\n" );
document.write( "solution, approximately what I got with a scientific calculator,\r\n" );
document.write( "x = -1.390957657.  However, your teacher cannot expect you to get\r\n" );
document.write( "that answer by hand, unless you use tedious iterative methods.\r\n" );
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document.write( "Edwin\r\n" );
document.write( "AnlytcPhil@aol.com

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