document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=733607>Question 733607</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the equation. Give all solutions (real or complex)\r<BR>\n" );
document.write( "\n" );
document.write( "2/(x+1)  -  4/(x+2) = 3x/x^2 + 3x+2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #448523 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=448523\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I assume you meant 2/(x+1) - 4/(x+2) = 3x/(x^2 + 3x+2) or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F%28x%2B1%29+-+4%2F%28x%2B2%29+=+3x%2F%28x%5E2+%2B+3x%2B2%29 ALIGN=MIDDLE  ALT=\"2%2F%28x%2B1%29+-+4%2F%28x%2B2%29+=+3x%2F%28x%5E2+%2B+3x%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B1%29%28x%2B2%29=x%5E3%2B3x%2B2 ALIGN=MIDDLE  ALT=\"%28x%2B1%29%28x%2B2%29=x%5E3%2B3x%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" > I would multiply both sides of the equation times that to get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28x%2B1%29%28x%2B2%29%2F%28x%2B1%29+-+4%28x%2B1%29%28x%2B2%29%2F%28x%2B2%29+=+3x%28x%2B1%29%28x%2B2%29%2F%28x%5E2+%2B+3x%2B2%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "That simplifies to<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28x%2B2%29-4%28x%2B1%29=3x ALIGN=MIDDLE  ALT=\"2%28x%2B2%29-4%28x%2B1%29=3x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Doing the indicated multiplications we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2B4-4x-4=3x ALIGN=MIDDLE  ALT=\"2x%2B4-4x-4=3x\"   DISABLED_style= \"max-width:90%; height:auto;\" > which simplifies to<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-4x=3x ALIGN=MIDDLE  ALT=\"2x-4x=3x\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-4x%2B4x-2x=3x%2B4x-2x ALIGN=MIDDLE  ALT=\"2x-4x%2B4x-2x=3x%2B4x-2x\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=5x ALIGN=MIDDLE  ALT=\"0=5x\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=0%29 ALIGN=MIDDLE  ALT=\"highlight%28x=0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "There are no more solutions.<BR>\n" );
document.write( "Verification:<BR>\n" );
document.write( "substituting 0 for x we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F1-4%2F2=0%2F2 ALIGN=MIDDLE  ALT=\"2%2F1-4%2F2=0%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2-2=0 ALIGN=MIDDLE  ALT=\"2-2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0 ALIGN=MIDDLE  ALT=\"x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a solution. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );