document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1182692>Question 1182692</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Give the integral of (2x)/(x^2+x-12) with respect to x. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #812775 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13215)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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/cgi-bin/show-face.mpl?user=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=812775\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Use partial fraction decomposition.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2F%28x%5E2%2B1-12%29+=+A%2F%28x%2B4%29%2BB%2F%28x-3%29 ALIGN=MIDDLE  ALT=\"2x%2F%28x%5E2%2B1-12%29+=+A%2F%28x%2B4%29%2BB%2F%28x-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Multiply through by the least common denominator:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x+=+A%28x-3%29%2BB%28x%2B4%29+=+%28A%2BB%29x%2B%284B-3A%29 ALIGN=MIDDLE  ALT=\"2x+=+A%28x-3%29%2BB%28x%2B4%29+=+%28A%2BB%29x%2B%284B-3A%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Equate the coefficients of the linear and constant terms on the two sides of the equation to get two equation to solve for A and B.<br><BR>\n" );
document.write( "A+B=2<BR>\n" );
document.write( "4B-3A=0<BR>\n" );
document.write( "3B+3A=6<BR>\n" );
document.write( "7B=6<BR>\n" );
document.write( "B=6/7<BR>\n" );
document.write( "A=8/7<br><BR>\n" );
document.write( "Rewrite the expression as the sum of two fractions with denominators that are linear polynomials:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2F%28x%5E2%2Bx-12%29+=+%286%2F7%29%2F%28x-3%29%2B%288%2F7%29%2F%28x%2B4%29 ALIGN=MIDDLE  ALT=\"2x%2F%28x%5E2%2Bx-12%29+=+%286%2F7%29%2F%28x-3%29%2B%288%2F7%29%2F%28x%2B4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Integrate using integral(1/(x-a))= log(x-a) plus a constant.<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );