document.write( "Question 1197127: Write an equation for a rational function with
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Algebra.Com's Answer #830252 by ikleyn(52835)\"\" \"About 
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\n" ); document.write( "Write an equation for a rational function with
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document.write( "Obviously, this rational function must have the binomial factors (x+5) and (x-6)\r\n" );
document.write( "in the denominator and binomial factors (x-2) and (x+2) in the numerator.\r\n" );
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document.write( "So, we write  \r\n" );
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document.write( "    y = \"%28a%2A%28x-2%29%2A%28x%2B2%29%29%2F%28%28x%2B5%29%2A%28x-6%29%29\" = \"%28a%2A%28x%5E2-4%29%29%2F%28%28%28x%2B5%29%2A%28x-6%29%29%29\".      (1)\r\n" );
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document.write( "Real coefficient \"a\" in the formula is intended to provide the necessary value y= 7 at x= 0.\r\n" );
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document.write( "To find \"a\", we equate function (1) to 7 at x= 0\r\n" );
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document.write( "    7 = \"%28a%2A%280%5E2-4%29%29%2F%28%280%2B5%29%2A%280-6%29%29\" = \"%28a%2A%28-4%29%29%2F%28-30%29\" = \"%282a%29%2F15\".\r\n" );
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document.write( "From this equation, we find \r\n" );
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document.write( "    a = \"%287%2A15%29%2F2\" = \"105%2F2\".\r\n" );
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document.write( "So, finally our function is\r\n" );
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document.write( "    y = \"%28105%2F2%29%2A%28%28x%5E2-4%29%2F%28%28x%2B5%29%2A%28x-6%29%29%29\".\r\n" );
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