document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=205151>Question 205151</A>: <I><SPAN STYLE=\"word-break: break-all;\"> i have an urgent question i dont know how to do ratioal functios that have an = sign in them!!!!! Will you please show me how to work out these two problems???? my problems are:  x+1/2x = x-1/2x-1 and\r<BR>\n" );
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document.write( "2/m^2-3m-4 = 2/3m+12 - m/m-1 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #154879 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=154879\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x+1/2x = x-1/2x-1<BR>\n" );
document.write( "Cross multiply<BR>\n" );
document.write( "(x+1)*(2x-1) = 2x*(x-1)<BR>\n" );
document.write( "2x^2 + x - 1 = 2x^2 - 2x<BR>\n" );
document.write( "x-1 = -2x<BR>\n" );
document.write( "3x = 1<BR>\n" );
document.write( "x = 1/3<BR>\n" );
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document.write( " and <BR>\n" );
document.write( "2/m^2+3m-4 = 2/3m+12 - m/m-1<BR>\n" );
document.write( "2/(m^2+3m-4) = 2/(3(m+4)) - m/m-1<BR>\n" );
document.write( "Are you sure the 1st term is not<BR>\n" );
document.write( "2/(m^2+3m-4) ??<BR>\n" );
document.write( "Poster confirmed via email that it's +, as below.<BR>\n" );
document.write( "2/(m^2+3m-4) = 2/(3(m+4)) - m/m-1<BR>\n" );
document.write( "2/(m+4)(m-1) = (2/3)/(m+4) - m/(m-1)<BR>\n" );
document.write( "6/(m+4)(m-1) = 2/(m+4) - 3m/(m-1)<BR>\n" );
document.write( "6/DEN = 2(m-1)/DEN - 3m(m+4)/DEN<BR>\n" );
document.write( "6 = 2(m-1) - 3m(m+4)<BR>\n" );
document.write( "6 = 2m-2 - 3m^2-12m<BR>\n" );
document.write( "3m^2 + 10m + 8 = 0<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%2B10x%2B8+=+0 ALIGN=MIDDLE  ALT=\"3x%5E2%2B10x%2B8+=+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=%2810%29%5E2-4%2A3%2A8=4 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%2810%29%5E2-4%2A3%2A8=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=4 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+=+%28-10%2B-sqrt%28+4+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-10%2B-sqrt%28+4+%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-%2810%29%2Bsqrt%28+4+%29%29%2F2%5C3+=+-1.33333333333333 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%2810%29%2Bsqrt%28+4+%29%29%2F2%5C3+=+-1.33333333333333\"   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-%2810%29-sqrt%28+4+%29%29%2F2%5C3+=+-2 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%2810%29-sqrt%28+4+%29%29%2F2%5C3+=+-2\"   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=3x%5E2%2B10x%2B8 ALIGN=MIDDLE  ALT=\"3x%5E2%2B10x%2B8\"   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%2B10x%2B8+=+%28x--1.33333333333333%29%2A%28x--2%29 ALIGN=MIDDLE  ALT=\"3x%5E2%2B10x%2B8+=+%28x--1.33333333333333%29%2A%28x--2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: -1.33333333333333, -2.\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%2B10%2Ax%2B8+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B10%2Ax%2B8+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( "==========================================<BR>\n" );
document.write( "m = -2<BR>\n" );
document.write( "m = -4/3\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );