document.write( "Question 152873: What is the equation of the slant asymptote for R(x) = x^2-6x+8/x-4?
\n" ); document.write( "a. R(x) = x – 2
\n" ); document.write( "b. R(x) = 1
\n" ); document.write( "c. R(x) = -5x + 2
\n" ); document.write( "d. There is no slant asymptote \n" ); document.write( "
Algebra.Com's Answer #112383 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
What is the equation of the slant asymptote for \"R%28x%29+=+%28x%5E2-6x%2B8%29%2F%28x-4%29\"?
\n" ); document.write( "a. \"R%28x%29+=+x+%96+2\"
\n" ); document.write( "b. \"R%28x%29+=+1\"
\n" ); document.write( "c. \"R%28x%29+=+-5x+%2B+2\"
\n" ); document.write( "d. There is no slant asymptote
\n" ); document.write( "
\r\n" );
document.write( "A rational function has a slant asymptote if and only if it meets\r\n" );
document.write( "both these conditions:\r\n" );
document.write( "\r\n" );
document.write( "1. The degree of the the numerator is 1 more than the degree of\r\n" );
document.write( "the denominator.\r\n" );
document.write( "\r\n" );
document.write( "2. When the denominator is divided into the numerator, a non-zero\r\n" );
document.write( "remainder is obtained.  \r\n" );
document.write( "\r\n" );
document.write( "3. If so then \"y+=+quotient\" is the equation of\r\n" );
document.write( "the slant asymptote.\r\n" );
document.write( "\r\n" );
document.write( "--------------------------------------\r\n" );
document.write( "\r\n" );
document.write( "\"R%28x%29+=+%28x%5E2-6x%2B8%29%2F%28x-4%29\"?\r\n" );
document.write( "\r\n" );
document.write( "The degree of the numerator is 2 (largest power of x is 2)\r\n" );
document.write( "The degree of the denominator is 1 (largest power of x is 1)\r\n" );
document.write( "\r\n" );
document.write( "Therefore it meets the first condition. Let's see if it meets\r\n" );
document.write( "the second condition:\r\n" );
document.write( "\r\n" );
document.write( "            x - 2\r\n" );
document.write( "x - 4)x² - 6x + 8\r\n" );
document.write( "      x² - 4x\r\n" );
document.write( "          -2x + 8\r\n" );
document.write( "          -2x + 8\r\n" );
document.write( "                0\r\n" );
document.write( "\r\n" );
document.write( "No, it leaves a zero remainder.  So R(x) does not have a\r\n" );
document.write( "slant asymptote.\r\n" );
document.write( "\r\n" );
document.write( "The correct choice is d\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );