document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=286145>Question 286145</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Will you please help me with this rational equation? I got it wrong on my test but still am having trouble solving it. I appreciate you taking the time to help me. \r<BR>\n" );
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document.write( "x/x^2-1+2/x-1=1+1/2x-2\r<BR>\n" );
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document.write( "I know the LCD is 2(x+1)(x-1). I multiplied every numerator by the missing factor and came up with totally the wrong answer. I am not sure what to do with the \"+1.\"\r<BR>\n" );
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document.write( "Tina  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #207478 by </B><A HREF=/tutors/aboutme.mpl?userid=oberobic><B>oberobic(2304)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=oberobic><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=207478\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F%28x%5E2-1%29%2B2%2F%28x-1%29=1%2B1%2F%282x-2%29 ALIGN=MIDDLE  ALT=\"x%2F%28x%5E2-1%29%2B2%2F%28x-1%29=1%2B1%2F%282x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-1+=+%28x%2B1%29%28x-1%29 ALIGN=MIDDLE  ALT=\"x%5E2-1+=+%28x%2B1%29%28x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-2+=+2%28x-1%29 ALIGN=MIDDLE  ALT=\"2x-2+=+2%28x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%28x%2B1%29%28x-1%29%2Ax%29%2F%28%28x%2B1%29%28x-1%29%29+%2B+2%28x%2B1%29%28x-1%29%2A2%2F%28x-1%29+=+2%2A%28x%2B1%29%28x-1%29%2A1+%2B+2%28x%2B1%29%28x-1%29%2A1%2F%282%28x-1%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The idea of the LCD is to get rid of the denominators...so cancel the terms you can:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2Ax%29+%2B+2%28x%2B1%29%2A2+=+2%2A%28x%2B1%29%28x-1%29%2A1+%2B+2%28x%2B1%29%2A1%2F%282%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Of course we can eliminate any '1' that is a multiplier, and cancel the 2/2.  And 2*2 is 4.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2x+%2B+4%28x%2B1%29+=+2%28x%2B1%29%28x-1%29+%2B+%28x%2B1%29+ ALIGN=MIDDLE  ALT=\"+2x+%2B+4%28x%2B1%29+=+2%28x%2B1%29%28x-1%29+%2B+%28x%2B1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2x+%2B+4x+%2B+4+=+2%28x%5E2+-1%29+%2B+x+%2B+1+ ALIGN=MIDDLE  ALT=\"+2x+%2B+4x+%2B+4+=+2%28x%5E2+-1%29+%2B+x+%2B+1+\"   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=+6x+%2B+4+=+2x%5E2+-2+%2B+x+%2B+1+ ALIGN=MIDDLE  ALT=\"+6x+%2B+4+=+2x%5E2+-2+%2B+x+%2B+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Subtract 6x from both sides.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4+=+2x%5E2+-2+%2B+x+%2B1+-6x+ ALIGN=MIDDLE  ALT=\"4+=+2x%5E2+-2+%2B+x+%2B1+-6x+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4+=+2x%5E2+-5x+-1+ ALIGN=MIDDLE  ALT=\"4+=+2x%5E2+-5x+-1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Subtract 4 from both sides.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+2x%5E2+-5x+-5+ ALIGN=MIDDLE  ALT=\"0+=+2x%5E2+-5x+-5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "This cannot be factored easily, so the quadratic equation can be used.<BR>\n" );
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document.write( "<TABLE  BORDER=1>\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=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=2x%5E2%2B-5x%2B-5+=+0 ALIGN=MIDDLE  ALT=\"2x%5E2%2B-5x%2B-5+=+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=%28-5%29%5E2-4%2A2%2A-5=65 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-5%29%5E2-4%2A2%2A-5=65\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=65 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--5%2B-sqrt%28+65+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--5%2B-sqrt%28+65+%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-%28-5%29%2Bsqrt%28+65+%29%29%2F2%5C2+=+3.26556443707464 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-5%29%2Bsqrt%28+65+%29%29%2F2%5C2+=+3.26556443707464\"   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-%28-5%29-sqrt%28+65+%29%29%2F2%5C2+=+-0.765564437074637 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-5%29-sqrt%28+65+%29%29%2F2%5C2+=+-0.765564437074637\"   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=2x%5E2%2B-5x%2B-5 ALIGN=MIDDLE  ALT=\"2x%5E2%2B-5x%2B-5\"   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-5x%2B-5+=+2%28x-3.26556443707464%29%2A%28x--0.765564437074637%29 ALIGN=MIDDLE  ALT=\"2x%5E2%2B-5x%2B-5+=+2%28x-3.26556443707464%29%2A%28x--0.765564437074637%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 3.26556443707464, -0.765564437074637.\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-5%2Ax%2B-5+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B-5%2Ax%2B-5+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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