document.write( "Question 1162547: Write the partial fraction decomposition of the following rational expression.
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Algebra.Com's Answer #853032 by MathTherapy(10587) $\"\"$ $\"About$

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document.write( "Write the partial fraction decomposition of the following rational expression.\r\n" );
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document.write( "The other person is WRONG!!\r\n" );
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document.write( " = \r\n" );
document.write( " =  --- Multiplying right-side by LCD, x(x + 4)(x + 5)\r\n" );
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document.write( " --- Equating NUMERATORS, since DENOMINATORS are same\r\n" );
document.write( " ------ Substituting - 5 for x, to determine the value of C\r\n" );
document.write( "8(25) - 50 + 20 = 0 + 0 + C(- 5)(- 5 + 4)\r\n" );
document.write( "  200 - 50 + 20 = C(- 5)(- 1)\r\n" );
document.write( "            170 = 5C\r\n" );
document.write( "            = 34 = C\r\n" );
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document.write( " ------ Substituting - 4 for x, to determine the value of B\r\n" );
document.write( "8(16) - 40 + 20 = 0 + B(- 4)(- 4 + 5) + 0\r\n" );
document.write( "  128 - 40 + 20 = B(- 4)(1)\r\n" );
document.write( "            108 = - 4B\r\n" );
document.write( "           = - 27 = B\r\n" );
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document.write( " ------ Substituting 1 for x, 34 for C, and - 27 for B, to determine the value of A\r\n" );
document.write( "8(1) + 10 + 20 = A(5)(6) - 27(1)(6) + 34(1)(5)\r\n" );
document.write( "   8 + 10 + 20 = 30A - 162 + 170\r\n" );
document.write( "            38 = 30A + 8\r\n" );
document.write( "        38 - 8 = 30A\r\n" );
document.write( "            30 = 30A\r\n" );
document.write( "            = 1 = A\r\n" );
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document.write( "So, (A, B, C)  = (1, - 27, 34)\r\n" );
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document.write( "We then get:  =  =

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