document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=172712>Question 172712</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If you could please help point me in the right direction!!! I need to solve this rational expression: <BR>\n" );
document.write( "2 + (4/x-5) = (15/x-4)\r<BR>\n" );
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document.write( "I have tried a couple of times, but seem to be off track. I know to find the \"LCD\" the multiply each side by that... i chose (x-5).\r<BR>\n" );
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document.write( "So then i have: [2(x-5)]/1 + [4(x-5)]/(x-5) = [15(x-5)]/(x-4)\r<BR>\n" );
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document.write( "I think that is what Im supposed to do, but then I get lost!! Is this the wrong way to apply the \"lcd\"?\r<BR>\n" );
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document.write( "Thank you SO much for your time, Im working on attempt #5... :)\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 #127560 by </B><A HREF=/tutors/aboutme.mpl?userid=Mathtut><B>Mathtut(3670)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Mathtut><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=127560\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> you need to multiply each term by (x-5)(x-4)<BR>\n" );
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document.write( "you should get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28x-4%29%28x-5%29%2B4%28x-4%29=15%28x-5%29 ALIGN=MIDDLE  ALT=\"2%28x-4%29%28x-5%29%2B4%28x-4%29=15%28x-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > distribute this<BR>\n" );
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document.write( "and end up with<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2-29x%2B99=0 ALIGN=MIDDLE  ALT=\"2x%5E2-29x%2B99=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<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=2x%5E2%2B-29x%2B99+=+0 ALIGN=MIDDLE  ALT=\"2x%5E2%2B-29x%2B99+=+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=%28-29%29%5E2-4%2A2%2A99=49 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-29%29%5E2-4%2A2%2A99=49\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=49 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--29%2B-sqrt%28+49+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--29%2B-sqrt%28+49+%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-%28-29%29%2Bsqrt%28+49+%29%29%2F2%5C2+=+9 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-29%29%2Bsqrt%28+49+%29%29%2F2%5C2+=+9\"   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-%28-29%29-sqrt%28+49+%29%29%2F2%5C2+=+5.5 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-29%29-sqrt%28+49+%29%29%2F2%5C2+=+5.5\"   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=2x%5E2%2B-29x%2B99 ALIGN=MIDDLE  ALT=\"2x%5E2%2B-29x%2B99\"   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=2x%5E2%2B-29x%2B99+=+%28x-9%29%2A%28x-5.5%29 ALIGN=MIDDLE  ALT=\"2x%5E2%2B-29x%2B99+=+%28x-9%29%2A%28x-5.5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 9, 5.5.\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+2%2Ax%5E2%2B-29%2Ax%2B99+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B-29%2Ax%2B99+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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