document.write( "Question 65353: [(x^2-4)/(x^2+3x-10)] / [(x^2+5x+6)/(x^2+8x+5)]\r
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Algebra.Com's Answer #45896 by Edwin McCravy(20060) $\"\"$ $\"About$

You can put this solution on YOUR website!
[(x^2-4)/(x^2+3x-10)] / [(x^2+5x+6)/(x^2+8x+5)]
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document.write( "Write it this way:\r\n" );
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document.write( "   x² - 4       x² + 5x + 6\r\n" );
document.write( "------------ ÷ -------------\r\n" );
document.write( "x² + 3x - 10    x² + 8x + 5\r\n" );
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document.write( "Invert the second fraction and change ÷ to ·\r\n" );
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document.write( "\r\n" );
document.write( "   x² - 4       x² + 8x + 5\r\n" );
document.write( "------------ · -------------\r\n" );
document.write( "x² + 3x - 10    x² + 5x + 6\r\n" );
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document.write( "Everything factors except the x² + 8x + 5.  \r\n" );
document.write( "Are you sure that + 5 shouldn't have been a\r\n" );
document.write( "+ 15?\r\n" );
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document.write( " (x - 2)(x + 2)       x² + 8x + 5\r\n" );
document.write( "---------------- · ----------------\r\n" );
document.write( " (x - 2)(x + 5)     (x + 3)(x + 2)\r\n" );
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document.write( "Indicate the multiplication of numerators\r\n" );
document.write( "and denominators, all as one fraction:\r\n" );
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document.write( " (x - 2)(x + 2)(x² + 8x + 5)\r\n" );
document.write( "------------------------------\r\n" );
document.write( " (x - 2)(x + 5)(x + 3)(x + 2)\r\n" );
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document.write( "Cancel the (x - 2)'s\r\n" );
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document.write( "    1      \r\n" );
document.write( " (x - 2)(x + 2)(x² + 8x + 5)\r\n" );
document.write( "------------------------------\r\n" );
document.write( " (x - 2)(x + 5)(x + 3)(x + 2)\r\n" );
document.write( "    1\r\n" );
document.write( "and cancel the (x + 2)'s\r\n" );
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document.write( "    1      1\r\n" );
document.write( " (x - 2)(x + 2)(x² + 8x + 5)\r\n" );
document.write( "------------------------------\r\n" );
document.write( " (x - 2)(x + 5)(x + 3)(x + 2)\r\n" );
document.write( "    1                    1\r\n" );
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document.write( "  x² + 8x + 5\r\n" );
document.write( "----------------\r\n" );
document.write( " (x + 5)(x + 3)\r\n" );
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document.write( "If that 5 on top had been a 15 the top \r\n" );
document.write( "would have factored exactly like the \r\n" );
document.write( "bottom and then everything would have \r\n" );
document.write( "canceled out and given the answer 1.\r\n" );
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document.write( "But as it is, nothing else will cancel\r\n" );
document.write( "and so you leave the answer just as it\r\n" );
document.write( "is. \r\n" );
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document.write( "Edwin

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