document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=985255>Question 985255</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do you solve <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+6+-%285%2F%28x%2B1%29%29+=+%286%2F%28x-3%29%29 ALIGN=MIDDLE  ALT=\"+6+-%285%2F%28x%2B1%29%29+=+%286%2F%28x-3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "I have tried this problem, but I go nowhere. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286x%2B6-5%29%2F%28x%2B1%29++=++%28-6%2F%28x-3%29%29 ALIGN=MIDDLE  ALT=\"%286x%2B6-5%29%2F%28x%2B1%29++=++%28-6%2F%28x-3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%28x%2B1%29%2F%28x%2B1%29+-+5%2F%28x%2B1%29 ALIGN=MIDDLE  ALT=\"6%28x%2B1%29%2F%28x%2B1%29+-+5%2F%28x%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #606073 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=606073\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> How do you solve <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+6+-%285%2F%28x%2B1%29%29+=+%286%2F%28x-3%29%29 ALIGN=MIDDLE  ALT=\"+6+-%285%2F%28x%2B1%29%29+=+%286%2F%28x-3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "I have tried this problem, but I go nowhere. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286x%2B6-5%29%2F%28x%2B1%29++=++-6%2F%28x-3%29 ALIGN=MIDDLE  ALT=\"%286x%2B6-5%29%2F%28x%2B1%29++=++-6%2F%28x-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > *** This is OK, except you changed the RHS to negative.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286x%2B6-5%29%2F%28x%2B1%29++=++6%2F%28x-3%29 ALIGN=MIDDLE  ALT=\"%286x%2B6-5%29%2F%28x%2B1%29++=++6%2F%28x-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286x%2B1%29%2F%28x%2B1%29++=++6%2F%28x-3%29 ALIGN=MIDDLE  ALT=\"%286x%2B1%29%2F%28x%2B1%29++=++6%2F%28x-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Cross multiply<BR>\n" );
document.write( "6(x+1) = (6x+1)*(x-3)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x+%2B+6+=+6x%5E2+-+17x+-+3 ALIGN=MIDDLE  ALT=\"6x+%2B+6+=+6x%5E2+-+17x+-+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x%5E2+-+23x+-+9+=+0 ALIGN=MIDDLE  ALT=\"6x%5E2+-+23x+-+9+=+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=6x%5E2%2B-23x%2B-9+=+0 ALIGN=MIDDLE  ALT=\"6x%5E2%2B-23x%2B-9+=+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=%28-23%29%5E2-4%2A6%2A-9=745 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-23%29%5E2-4%2A6%2A-9=745\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=745 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--23%2B-sqrt%28+745+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--23%2B-sqrt%28+745+%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-%28-23%29%2Bsqrt%28+745+%29%29%2F2%5C6+=+4.19122401065936 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-23%29%2Bsqrt%28+745+%29%29%2F2%5C6+=+4.19122401065936\"   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-%28-23%29-sqrt%28+745+%29%29%2F2%5C6+=+-0.35789067732603 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-23%29-sqrt%28+745+%29%29%2F2%5C6+=+-0.35789067732603\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <BR>\n" );
document.write( "    Quadratic expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x%5E2%2B-23x%2B-9 ALIGN=MIDDLE  ALT=\"6x%5E2%2B-23x%2B-9\"   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=6x%5E2%2B-23x%2B-9+=+%28x-4.19122401065936%29%2A%28x--0.35789067732603%29 ALIGN=MIDDLE  ALT=\"6x%5E2%2B-23x%2B-9+=+%28x-4.19122401065936%29%2A%28x--0.35789067732603%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 4.19122401065936, -0.35789067732603.\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+6%2Ax%5E2%2B-23%2Ax%2B-9+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+6%2Ax%5E2%2B-23%2Ax%2B-9+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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