document.write( "Question 621023: a) f(x)= x^2-1/x(x=2)
\n" ); document.write( "find the partial fraction of f(x)\r
\n" ); document.write( "\n" ); document.write( "b) Solve f(x)>0, hence write the solution for f(x)<0
\n" ); document.write( "Solution of the question need show in line and also table as well.
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Algebra.Com's Answer #390525 by Edwin McCravy(20086) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "f(x) =  \r\n" );
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document.write( "When the degree of the numerator is greater than or equal to the\r\n" );
document.write( "degree of the denominator, the fraction must be divided out first\r\n" );
document.write( "by long division:\r\n" );
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document.write( "  = \r\n" );
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document.write( "                      1\r\n" );
document.write( "x² - 2x + 0)x² - 0x - 1\r\n" );
document.write( "            x² - 2x + 0\r\n" );
document.write( "                 2x - 1\r\n" );
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document.write( "f(x) = 1 +  = 1 + \r\n" );
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document.write( "f(x) = 1 +  = 1 +  + \r\n" );
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document.write( " =  + \r\n" );
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document.write( "2x-1 = A(x-2) + Bx\r\n" );
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document.write( "This must be true for all values of x so we choose x=2\r\n" );
document.write( "so the first term on the right will be 0\r\n" );
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document.write( "2(2)-1 = A(2-2) + B(2)\r\n" );
document.write( " 4 - 1 = A(0) + 2B\r\n" );
document.write( "     3 = 0 + 2B\r\n" );
document.write( "     3 = 2B\r\n" );
document.write( "      = B\r\n" );
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document.write( "Now we choose x=0 so the second term on the right will be 0\r\n" );
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document.write( "2(0)-1 = A(0-2) + B(0)\r\n" );
document.write( "   0-1 = A(-2) + 0\r\n" );
document.write( "    -1 = -2A \r\n" );
document.write( "     = A\r\n" );
document.write( "     = A\r\n" );
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document.write( " +  =  +  = · + · =  + \r\n" );
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document.write( "Therefore f(x) =  = 1 +  + \r\n" );
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document.write( "Edwin

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