document.write( "Question 55883: x^2-1/x^2+x*3x/1-x please help simplify \n" ); document.write( "
Algebra.Com's Answer #37886 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
x^2-1/x^2+x*3x/1-x please help simplify\r\n" );
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document.write( " x² - 1       3x\r\n" );
document.write( "-------- · -------\r\n" );
document.write( " x² + x     1 - x\r\n" );
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document.write( "All the numerators and denominators\r\n" );
document.write( "are in descending order except 1 - x\r\n" );
document.write( "So arrange the 1 - x in descending order,\r\n" );
document.write( "as -x + 1\r\n" );
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document.write( " x² - 1       3x\r\n" );
document.write( "-------- · -------\r\n" );
document.write( " x² + x     -x + 1  \r\n" );
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document.write( "Factor the upper left numerator as the\r\n" );
document.write( "difference of two squares:\r\n" );
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document.write( " (x - 1)(x + 1)       3x\r\n" );
document.write( "---------------- · --------\r\n" );
document.write( "     x² + x         -x + 1\r\n" );
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document.write( "Factor the lower left denominator by\r\n" );
document.write( "factoring out x\r\n" );
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document.write( " (x - 1)(x + 1)       3x\r\n" );
document.write( "---------------- · --------\r\n" );
document.write( "     x(x + 1)       -x + 1 \r\n" );
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document.write( "Factor the lower right denominator by\r\n" );
document.write( "factoring out -1, which causes a \r\n" );
document.write( "sign change inside the parentheses:\r\n" );
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document.write( " (x - 1)(x + 1)       3x\r\n" );
document.write( "---------------- · ----------\r\n" );
document.write( "     x(x + 1)      -1(x - 1)\r\n" );
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document.write( "Indicate the multiplication of the\r\n" );
document.write( "numerators and denominators so that\r\n" );
document.write( "we have just one fraction. Write the\r\n" );
document.write( "shorter factors first:\r\n" );
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document.write( "     3x(x - 1)(x + 1)      \r\n" );
document.write( "   -------------------\r\n" );
document.write( "    -1x(x + 1)(x - 1)\r\n" );
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document.write( " Cancel the x's\r\n" );
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document.write( "      1\r\n" );
document.write( "     3x(x - 1)(x + 1)      \r\n" );
document.write( "   -------------------\r\n" );
document.write( "    -1x(x + 1)(x - 1)\r\n" );
document.write( "      1\r\n" );
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document.write( "Cancel the (x - 1)'s\r\n" );
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document.write( "      1   1\r\n" );
document.write( "     3x(x - 1)(x + 1)      \r\n" );
document.write( "   -------------------\r\n" );
document.write( "    -1x(x + 1)(x - 1)\r\n" );
document.write( "      1          1\r\n" );
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document.write( "Cancel the (x + 1)'s\r\n" );
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document.write( "      1   1      1\r\n" );
document.write( "     3x(x - 1)(x + 1)      \r\n" );
document.write( "   -------------------\r\n" );
document.write( "    -1x(x + 1)(x - 1)\r\n" );
document.write( "      1   1      1\r\n" );
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document.write( "All that's left is\r\n" );
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document.write( "     3\r\n" );
document.write( "   ----\r\n" );
document.write( "    -1\r\n" );
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document.write( "which is just\r\n" );
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document.write( "    -3\r\n" );
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document.write( "Edwin
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