document.write( "Question 637491: Write the partial fraction decomposition of the rational expression:
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Algebra.Com's Answer #401728 by Edwin McCravy(20056) $\"\"$ $\"About$

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document.write( "We write the sum of all fractions with a denominator which is a\r\n" );
document.write( "divisor of the denominator:\r\n" );
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document.write( " =  +  + \r\n" );
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document.write( "Clear of fractions:\r\n" );
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document.write( "4x² + 2x - 1 = Ax(x+1) + B(x+1) + Cx²\r\n" );
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document.write( "Substitute x=-1 to make the (x+1)'s 0\r\n" );
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document.write( "4(-1)² + 2(-1) - 1 = A(-1)(-1+1) + B(-1+1) + C(-1)²\r\n" );
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document.write( "4(1) - 2 - 1 = A(-1)(0) + B(0) + C(1)\r\n" );
document.write( "   4 - 2 - 1 = 0 + 0 + C\r\n" );
document.write( "           1 = C\r\n" );
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document.write( "Substitute x=0 to make the 1st and 3rd terms on the right 0:\r\n" );
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document.write( "4x² + 2x - 1 = Ax(x+1) + B(x+1) + Cx²\r\n" );
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document.write( "4(0)² + 2(0) - 1 = A(0)(0+1) + B(0+1) + C(0)\r\n" );
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document.write( "0 + 0 - 1 = A(0)(1) + B(1) + 0\r\n" );
document.write( "       -1 = 0 + B\r\n" );
document.write( "       -1 = B\r\n" );
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document.write( "Substitute B = -1 and C = 1\r\n" );
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document.write( "4x² + 2x - 1 = Ax(x+1) + (-1)(x+1) + (1)x²\r\n" );
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document.write( "4x² + 2x - 1 = Ax(x+1) - (x+1) + x²\r\n" );
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document.write( "Substitute x=1  (Note: we could use ANY number here that we haven't used):\r\n" );
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document.write( "4(1)² + 2(1) - 1 = A(1)(1+1) - (1+1) + 1²\r\n" );
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document.write( " 4 + 2 - 1 = 2A - 2 + 1\r\n" );
document.write( "         5 = 2A - 1\r\n" );
document.write( "         6 = 2A\r\n" );
document.write( "         3 = A\r\n" );
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document.write( "So A = 3, B = -1, C = 1\r\n" );
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document.write( "Answer:\r\n" );
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document.write( " =  -  + \r\n" );
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document.write( "Edwin

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