document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1031718>Question 1031718</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the equation by using the LCD.<BR>\n" );
document.write( "I don't know how to do this one, it look confusing \r<BR>\n" );
document.write( "\n" );
document.write( "(5) / (x^2+x-6) = (2) + (x-3) / (x-2) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #646477 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=646477\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 5/(x^2+x-6) = 2 + (x-3)/(x-2)<BR>\n" );
document.write( "x^2+x-6 can be factored.<BR>\n" );
document.write( "---<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F%28%28x%2B3%29%2A%28x-2%29%29+=+2+%2B+%28x-3%29%2F%28x-2%29 ALIGN=MIDDLE  ALT=\"5%2F%28%28x%2B3%29%2A%28x-2%29%29+=+2+%2B+%28x-3%29%2F%28x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "LCD = (x+3)*(x-2)<BR>\n" );
document.write( "---<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F%28%28x%2B3%29%2A%28x-2%29%29+=+2+%2B+%28x-3%29%2A%28x%2B3%29%2FLCD ALIGN=MIDDLE  ALT=\"5%2F%28%28x%2B3%29%2A%28x-2%29%29+=+2+%2B+%28x-3%29%2A%28x%2B3%29%2FLCD\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Multiply thru by DEN, the LCD<BR>\n" );
document.write( "5 = 2*(x^2+x-6) + (x-3)*(x+3)<BR>\n" );
document.write( "5 = 3x^2 + 2x - 21<BR>\n" );
document.write( "3x^2 + 2x - 26 = 0<BR>\n" );
document.write( "<TABLE  BORDER=1>\n" );
document.write( "\n" );
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%2B2x%2B-26+=+0 ALIGN=MIDDLE  ALT=\"3x%5E2%2B2x%2B-26+=+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=%282%29%5E2-4%2A3%2A-26=316 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%282%29%5E2-4%2A3%2A-26=316\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=316 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+=+%28-2%2B-sqrt%28+316+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-2%2B-sqrt%28+316+%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-%282%29%2Bsqrt%28+316+%29%29%2F2%5C3+=+2.6293981391052 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%282%29%2Bsqrt%28+316+%29%29%2F2%5C3+=+2.6293981391052\"   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-%282%29-sqrt%28+316+%29%29%2F2%5C3+=+-3.29606480577186 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%282%29-sqrt%28+316+%29%29%2F2%5C3+=+-3.29606480577186\"   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%2B2x%2B-26 ALIGN=MIDDLE  ALT=\"3x%5E2%2B2x%2B-26\"   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%2B2x%2B-26+=+%28x-2.6293981391052%29%2A%28x--3.29606480577186%29 ALIGN=MIDDLE  ALT=\"3x%5E2%2B2x%2B-26+=+%28x-2.6293981391052%29%2A%28x--3.29606480577186%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 2.6293981391052, -3.29606480577186.\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%2B2%2Ax%2B-26+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B2%2Ax%2B-26+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
document.write( "\n" );
document.write( "==========================\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );