document.write( "Question 1146014: 1. (a) resolve into partial fractions 2x/[(x-2)(x+5)]
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Algebra.Com's Answer #853008 by MathTherapy(10579)\"\" \"About 
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document.write( "1. (a) resolve into partial fractions 2x/[(x-2)(x+5)]\r\n" );
document.write( "   (b) resolve into partial fractions 1/(x^2-x)\r\n" );
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document.write( "1. (a) resolve into partial fractions \"2x%2F%28x+-+2%29%28x+%2B+5%29\"\r\n" );
document.write( "The other person’s solution: A = \"2%2F3\", and B = \"4%2F3\", is WRONG!!\r\n" );
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document.write( "\"2x%2F%28x+-+2%29%28x+%2B+5%29\" = \"A%2F%28x+-+2%29+%2B+B%2F%28x+%2B+5%29\"\r\n" );
document.write( " ---- Multiplying by LCD, (x - 2)(x + 5)\r\n" );
document.write( "           2x = A(x + 5) + B(x - 2) ---- Equating NUMERATORS, since denominators are the same\r\n" );
document.write( "         2(2) = A(2 + 5) + B(2 - 2) ---- Substituting 2 for x to determine the value of A\r\n" );
document.write( "            4 = 7A\r\n" );
document.write( "                \"4%2F7+=+A\"\r\n" );
document.write( "       2(- 5) = A(- 5 + 5) + B(- 5 - 2) ---- Substituting - 5 for x to determine the value of B\r\n" );
document.write( "         - 10 = - 7B\r\n" );
document.write( "        \"%28-+10%29%2F%28-+7%29+=+10%2F7+=+B\"\r\n" );
document.write( "       (A, B) = (\"4%2F7\", \"10%2F7\")\r\n" );
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document.write( "Therefore, \"highlight%282x%2F%28x+-+2%29%28x+%2B+5%29%29\" = \"A%2F%28x+-+2%29+%2B+B%2F%28x+%2B+5%29\" = \"highlight%28%284%2F7%29%2F%28x+-+2%29+%2B+%2810%2F7%29%2F%28x+%2B+5%29%29\"\r\n" );
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document.write( "1. (b) resolve into partial fractions \"1%2F%28x%5E2+-+x%29\"\r\n" );
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document.write( "Use the same concept above, to decompose this PROPER FRACTION too. \r\n" );
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document.write( "Before doing so though, we FACTORIZE the denominator in \"1%2F%28x%5E2+-+x%29\" to get: \"1%2Fx%28x+-+1%29\", and then: \"1%2Fx%28x+-+1%29\" = \"A%2Fx+%2B+B%2F%28x+-+1%29\"
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