document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=209055>Question 209055</A>: <I><SPAN STYLE=\"word-break: break-all;\"> use partial functions to decompose the expression 17n-23 / 4n^2+23n-6 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #158033 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=158033\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> use partial functions to decompose the expression 17n-23 / 4n^2+23n-6<BR>\n" );
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document.write( "Factor the denominator to get (n+6)(4n-1)<BR>\n" );
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document.write( "Set up the partial fractions:<BR>\n" );
document.write( "A/(n+6) + B/(4n-1)<BR>\n" );
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document.write( "Simplify:<BR>\n" );
document.write( "[A(4n-1) + B(n+6)]/(4n^2+23n-6)<BR>\n" );
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document.write( "[4An + Bn -A + 6B]/ denominator\r<BR>\n" );
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document.write( "= [ (4A+B)n + (-A+6B)]/denom\r<BR>\n" );
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document.write( "Equate to the original fraction to see that<BR>\n" );
document.write( "4A+B = 17<BR>\n" );
document.write( "-A+6B = -23<BR>\n" );
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document.write( "Solve this system to get:<BR>\n" );
document.write( "A = 5 <BR>\n" );
document.write( "B = -3<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( "Reply to stanbon@comcast.net or algebra.com\r<BR>\n" );
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document.write( " </SPAN>\n" );
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