document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=705278>Question 705278</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need to solve for x and show work --> (2/x-2)=(4/x-3)-(1/x+1) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #434491 by </B><A HREF=/tutors/aboutme.mpl?userid=Stitch><B>Stitch(470)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Stitch><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=434491\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given:: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F%28X-1%29+=+4%2F%28X-3%29+-+1%2F%28X%2B1%29 ALIGN=MIDDLE  ALT=\"2%2F%28X-1%29+=+4%2F%28X-3%29+-+1%2F%28X%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "I would start by multiplying everything by each of the denominators<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F%28X-1%29%2A%28X-1%29%2A%28X-3%29%2A%28X%2B1%29+=+4%2F%28X-3%29%2A%28X-1%29%2A%28X-3%29%2A%28X%2B1%29+-+1%2F%28X%2B1%29%2A%28X-1%29%2A%28X-3%29%2A%28X%2B1%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Then the denominators will cancel out<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Fcross%28%28X-1%29%29%2Across%28%28X-1%29%29%2A%28X-3%29%2A%28X%2B1%29+=+4%2Fcross%28%28X-3%29%29%2A%28X-1%29%2Across%28%28X-3%29%29%2A%28X%2B1%29+-+1%2Fcross%28%28X%2B1%29%29%2A%28X-1%29%2A%28X-3%29%2Across%28%28X%2B1%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Rewrite the equation.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2A%28X-3%29%2A%28X%2B1%29+=+4%2A%28X-1%29%2A%28X%2B1%29+-+1%2A%28X-1%29%2A%28X-3%29 ALIGN=MIDDLE  ALT=\"2%2A%28X-3%29%2A%28X%2B1%29+=+4%2A%28X-1%29%2A%28X%2B1%29+-+1%2A%28X-1%29%2A%28X-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Start to multiply through<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282X+-+6%29%2A%28X%2B1%29+=+%284X-4%29%2A%28X%2B1%29+%2B+%28-X%2B1%29%2A%28X-3%29 ALIGN=MIDDLE  ALT=\"%282X+-+6%29%2A%28X%2B1%29+=+%284X-4%29%2A%28X%2B1%29+%2B+%28-X%2B1%29%2A%28X-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Multiply through<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2X%5E2+%2B+2X+-+6X+-+6+=+4X%5E2+%2B+4X+-+4X+-+4+-+X%5E2+%2B+3X+%2B+X+-+3 ALIGN=MIDDLE  ALT=\"2X%5E2+%2B+2X+-+6X+-+6+=+4X%5E2+%2B+4X+-+4X+-+4+-+X%5E2+%2B+3X+%2B+X+-+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Combine like terms<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2X%5E2+-+4X+-+6+=+3X%5E2+%2B+4X+-+7 ALIGN=MIDDLE  ALT=\"2X%5E2+-+4X+-+6+=+3X%5E2+%2B+4X+-+7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Subtract 2X^2 from both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4X+-+6+=+X%5E2+%2B+4X+-+7 ALIGN=MIDDLE  ALT=\"-4X+-+6+=+X%5E2+%2B+4X+-+7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Add 4X to both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6+=+X%5E2+%2B+8X+-+7 ALIGN=MIDDLE  ALT=\"-6+=+X%5E2+%2B+8X+-+7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Add 6 to both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+X%5E2+%2B+8X+-+1 ALIGN=MIDDLE  ALT=\"0+=+X%5E2+%2B+8X+-+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now use the quadratic equation.<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=quadratic.solver>SOLVE quadratic equation with variable</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=1X%5E2%2B8X%2B-1+=+0 ALIGN=MIDDLE  ALT=\"1X%5E2%2B8X%2B-1+=+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=%288%29%5E2-4%2A1%2A-1=68 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%288%29%5E2-4%2A1%2A-1=68\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=68 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+=+%28-8%2B-sqrt%28+68+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-8%2B-sqrt%28+68+%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-%288%29%2Bsqrt%28+68+%29%29%2F2%5C1+=+0.123105625617661 ALIGN=MIDDLE  ALT=\"X%5B1%5D+=+%28-%288%29%2Bsqrt%28+68+%29%29%2F2%5C1+=+0.123105625617661\"   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-%288%29-sqrt%28+68+%29%29%2F2%5C1+=+-8.12310562561766 ALIGN=MIDDLE  ALT=\"X%5B2%5D+=+%28-%288%29-sqrt%28+68+%29%29%2F2%5C1+=+-8.12310562561766\"   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=1X%5E2%2B8X%2B-1 ALIGN=MIDDLE  ALT=\"1X%5E2%2B8X%2B-1\"   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=1X%5E2%2B8X%2B-1+=+1%28X-0.123105625617661%29%2A%28X--8.12310562561766%29 ALIGN=MIDDLE  ALT=\"1X%5E2%2B8X%2B-1+=+1%28X-0.123105625617661%29%2A%28X--8.12310562561766%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 0.123105625617661, -8.12310562561766.\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+1%2Ax%5E2%2B8%2Ax%2B-1+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B8%2Ax%2B-1+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
document.write( "\n" );
document.write( "So X = 0.1231 & -8.1231 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );