document.write( "Question 87275: Please help me solve the following equations:\r
\n" ); document.write( "\n" ); document.write( "Reduce each expression to the lowest terms:\r
\n" ); document.write( "\n" ); document.write( "78) \"%284x%5E2%29%2F%282x%5E9%29\"\r
\n" ); document.write( "\n" ); document.write( "88) \"%28-2x-8%29%2F%28x%5E2%2B2x-8%29\"\r
\n" ); document.write( "\n" ); document.write( "Thank you very much!\r
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Algebra.Com's Answer #63214 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Please help me solve the following equations: \r\n" );
document.write( "Reduce each expression to the lowest terms: \r\n" );
document.write( "78)  \r\n" );
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document.write( "     4x2\r\n" );
document.write( "    -----\r\n" );
document.write( "     2x9\r\n" );
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document.write( "Divide the 4 and the 2 each by 2\r\n" );
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document.write( "     2 \r\n" );
document.write( "     4x2\r\n" );
document.write( "    -----\r\n" );
document.write( "     2x9\r\n" );
document.write( "     1\r\n" );
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document.write( "or\r\n" );
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document.write( "     2x2\r\n" );
document.write( "    -----\r\n" );
document.write( "      x9\r\n" );
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document.write( "Now subtract exponents according to this rule:\r\n" );
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document.write( "1. Subtract \"larger exponent minus smaller exponent\"\r\n" );
document.write( "2. Place that power of the base in the numerator IF\r\n" );
document.write( "   the larger exonent was in the numerator or place\r\n" );
document.write( "   it in the denominator if the larger exponent was\r\n" );
document.write( "   in the denominator.\r\n" );
document.write( "3. Eliminate the base and exponent in the numerator\r\n" );
document.write( "   or denominator wherever the smaller exponent was.\r\n" );
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document.write( "In this case the larger exponent, 9, is in the \r\n" );
document.write( "denominator, so we subtract exponents 9-2 getting\r\n" );
document.write( "7 and place x7 in the denominator, and we then\r\n" );
document.write( "eliminate x altogether from the numerator, where\r\n" );
document.write( "the smaller exponent 2 was:\r\n" );
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document.write( "     4\r\n" );
document.write( "    ---\r\n" );
document.write( "     x7  \r\n" );
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document.write( "That's the final answer.\r\n" );
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document.write( "======================\r\n" );
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document.write( "88)  \r\n" );
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document.write( "  -2x-8\r\n" );
document.write( "---------\r\n" );
document.write( " x2+2x-8\r\n" );
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document.write( "Factor the numerator by taking out -2\r\n" );
document.write( "Factor the denominator as a binomial\r\n" );
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document.write( "   -2(x+4)\r\n" );
document.write( "------------\r\n" );
document.write( " (x+4)(x-2)\r\n" );
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document.write( "Cancel the (x+4)'s\r\n" );
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document.write( "       1\r\n" );
document.write( "   -2(x+4)\r\n" );
document.write( "------------\r\n" );
document.write( " (x+4)(x-2)\r\n" );
document.write( "   1\r\n" );
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document.write( "That leaves\r\n" );
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document.write( " -2\r\n" );
document.write( "-----\r\n" );
document.write( " x-2 \r\n" );
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document.write( "Your teacher will probably\r\n" );
document.write( "expect you to stop there, and\r\n" );
document.write( "give that as the final answer\r\n" );
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document.write( "----------------------------   \r\n" );
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document.write( "However you can write it\r\n" );
document.write( "simpler by multiplying\r\n" );
document.write( "numerator and denominator \r\n" );
document.write( "by (-1):\r\n" );
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document.write( "   -2(-1)\r\n" );
document.write( "------------\r\n" );
document.write( " (x-2)(-1)\r\n" );
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document.write( "   2\r\n" );
document.write( "---------\r\n" );
document.write( " -1(x-2)\r\n" );
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document.write( "   2\r\n" );
document.write( "------\r\n" );
document.write( " -x+2\r\n" );
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document.write( "Then reverse the two terms\r\n" );
document.write( "in the denominator:\r\n" );
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document.write( "  2\r\n" );
document.write( "-----\r\n" );
document.write( " 2-x\r\n" );
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document.write( "which is a tiny bit simpler.\r\n" );
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document.write( "Edwin
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