document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=202332>Question 202332</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve equation:\r<BR>\n" );
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document.write( "(x+1/x-1) + (2/x)= (x/x+1)\r<BR>\n" );
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document.write( "How do I solve this? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #152571 by </B><A HREF=/tutors/aboutme.mpl?userid=dyakobovitch><B>dyakobovitch(40)</B></A><img src=\"/images/stars/stars-07.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=dyakobovitch><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=152571\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> For the equation, (x+1/x-1) + (2/x)= (x/x+1), your first step is to eliminate your denominator. This can be done by looking for the least common multiple of x, (x-1), and (x+1), which happens to be x(x-1)(x+1). \r<BR>\n" );
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document.write( "As such, you want to multiply all three parts of your equation by x(x-1)(x+1). This multiplication preserves the equality of the equation. Your result is x(x-1)(x+1)(x+1)/(x-1) + 2x(x-1)(x+1)/x= x^2(x-1)(x+1)/(x+1), which simplifies to x(x+1)^2 + 2(x-1)(x+1)= x^2(x-1). \r<BR>\n" );
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document.write( "Simplifying the quadratic equation, you get x^3+2x^2+x +2x^2-2=x^3-x^2. Your new quadratic equation becomes 5x^2+x-2=0. <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=5x%5E2%2B1x%2B-2+=+0 ALIGN=MIDDLE  ALT=\"5x%5E2%2B1x%2B-2+=+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=%281%29%5E2-4%2A5%2A-2=41 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%281%29%5E2-4%2A5%2A-2=41\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=41 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+=+%28-1%2B-sqrt%28+41+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-1%2B-sqrt%28+41+%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-%281%29%2Bsqrt%28+41+%29%29%2F2%5C5+=+0.540312423743285 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%281%29%2Bsqrt%28+41+%29%29%2F2%5C5+=+0.540312423743285\"   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-%281%29-sqrt%28+41+%29%29%2F2%5C5+=+-0.740312423743285 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%281%29-sqrt%28+41+%29%29%2F2%5C5+=+-0.740312423743285\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "    Quadratic expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%5E2%2B1x%2B-2 ALIGN=MIDDLE  ALT=\"5x%5E2%2B1x%2B-2\"   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=5x%5E2%2B1x%2B-2+=+5%28x-0.540312423743285%29%2A%28x--0.740312423743285%29 ALIGN=MIDDLE  ALT=\"5x%5E2%2B1x%2B-2+=+5%28x-0.540312423743285%29%2A%28x--0.740312423743285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 0.540312423743285, -0.740312423743285.\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+5%2Ax%5E2%2B1%2Ax%2B-2+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+5%2Ax%5E2%2B1%2Ax%2B-2+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( ". </SPAN>\n" );
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