document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=634967>Question 634967</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have tried many different ways to solve this equation and I just can't seem to get it right:\r<BR>\n" );
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document.write( "                      5/3x-8=x/x+2\r<BR>\n" );
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document.write( "I know I have to cross multiply but when I do that I end up with this:<BR>\n" );
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document.write( "                        5x+10=3x^2-8x\r<BR>\n" );
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document.write( "I don't really know where to go from there. If I add 8x to 5x then it seems like that's all the simplifying I can do, unless I subtract 3x^2 and somehow turn it into a quadratic formula, but that also doesn't seem right. I also tried to see if I could just cross out the x's on x/x+2 but then that would leave me with 0/2 (simply just a zero) and then I would just have 5/3x-8. Where would I go from there? And I don't think that the answer is still supposed to have variables, I think that it is a number, but I just don't see how that is possible. Please help! Thank you so much.\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #400023 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=400023\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I have tried many different ways to solve this equation and I just can't seem to get it right:\r<BR>\n" );
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document.write( "                      5/3x-8=x/x+2<BR>\n" );
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document.write( "If you mean<BR>\n" );
document.write( "5/(3x-8) = x/(x+2)<BR>\n" );
document.write( "Cross multiply<BR>\n" );
document.write( "5(x+2) = x(3x-8)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%2B10+=+3x%5E2+-+8x ALIGN=MIDDLE  ALT=\"5x%2B10+=+3x%5E2+-+8x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2+-+13x+-+10+=+0 ALIGN=MIDDLE  ALT=\"3x%5E2+-+13x+-+10+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=solve_quadratic_equation.solver>SOLVE quadratic equation (work shown, graph etc)</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Quadratic equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2%2Bbx%2Bc=0 ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2%2B-13x%2B-10+=+0 ALIGN=MIDDLE  ALT=\"3x%5E2%2B-13x%2B-10+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >) has the following solutons:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  For these solutions to exist, the <U>discriminant</U> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" > should not be a negative number.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  First, we need to compute the discriminant <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" >: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac=%28-13%29%5E2-4%2A3%2A-10=289 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-13%29%5E2-4%2A3%2A-10=289\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "  Discriminant d=289 is greater than zero. That means that there are two solutions: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5B12%5D+=+%28--13%2B-sqrt%28+289+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--13%2B-sqrt%28+289+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D+=+%28-%28-13%29%2Bsqrt%28+289+%29%29%2F2%5C3+=+5 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-13%29%2Bsqrt%28+289+%29%29%2F2%5C3+=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D+=+%28-%28-13%29-sqrt%28+289+%29%29%2F2%5C3+=+-0.666666666666667 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-13%29-sqrt%28+289+%29%29%2F2%5C3+=+-0.666666666666667\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "    Quadratic expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2%2B-13x%2B-10 ALIGN=MIDDLE  ALT=\"3x%5E2%2B-13x%2B-10\"   DISABLED_style= \"max-width:90%; height:auto;\" > can be factored:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2%2B-13x%2B-10+=+%28x-5%29%2A%28x--0.666666666666667%29 ALIGN=MIDDLE  ALT=\"3x%5E2%2B-13x%2B-10+=+%28x-5%29%2A%28x--0.666666666666667%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 5, -0.666666666666667.\n" );
document.write( "Here's your graph:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B-13%2Ax%2B-10+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B-13%2Ax%2B-10+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( "=================<BR>\n" );
document.write( "Does that work?\r<BR>\n" );
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