document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=110861>Question 110861</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1.  If x + a/x = b then find the value of (x^2 + bx + a)/(bx^2 - x^3)  \r<BR>\n" );
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document.write( "2.  If x + 1/x = 99, find the value of 100x/(3x^2 + 103x + 3)\r<BR>\n" );
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document.write( "Question from Tata Mc Graw-Hill NTSE book </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #80865 by </B><A HREF=/tutors/aboutme.mpl?userid=edjones><B>edjones(8007)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=edjones><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=edjones><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=80865\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x + a/x = b<BR>\n" );
document.write( "(x^2 + bx + a)/(bx^2 - x^3) <BR>\n" );
document.write( "(x^2+x(x + a/x)+a/(x^2(x + a/x )-x^3<BR>\n" );
document.write( "(x^2+x^2 + a +a)/(x^3 + ax -x^3)<BR>\n" );
document.write( "(2x^2+2a)/ax<BR>\n" );
document.write( ".<BR>\n" );
document.write( "x + 1/x = 99<BR>\n" );
document.write( "x^2+1=99x eliminate fractions multiply each side by x<BR>\n" );
document.write( "x^2-99x+1=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=1x%5E2%2B-99x%2B1+=+0 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-99x%2B1+=+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=%28-99%29%5E2-4%2A1%2A1=9797 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-99%29%5E2-4%2A1%2A1=9797\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=9797 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--99%2B-sqrt%28+9797+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--99%2B-sqrt%28+9797+%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-%28-99%29%2Bsqrt%28+9797+%29%29%2F2%5C1+=+98.9898979590785 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-99%29%2Bsqrt%28+9797+%29%29%2F2%5C1+=+98.9898979590785\"   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-%28-99%29-sqrt%28+9797+%29%29%2F2%5C1+=+0.0101020409215238 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-99%29-sqrt%28+9797+%29%29%2F2%5C1+=+0.0101020409215238\"   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=1x%5E2%2B-99x%2B1 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-99x%2B1\"   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%2B-99x%2B1+=+%28x-98.9898979590785%29%2A%28x-0.0101020409215238%29 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-99x%2B1+=+%28x-98.9898979590785%29%2A%28x-0.0101020409215238%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 98.9898979590785, 0.0101020409215238.\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%2B-99%2Ax%2B1+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-99%2Ax%2B1+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28500%2C500%2C-10%2C110%2C-3000%2C1000%2Cx%5E2-99x%2B1%29 ALIGN=MIDDLE  ALT=\"graph%28500%2C500%2C-10%2C110%2C-3000%2C1000%2Cx%5E2-99x%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "I'll let you plug the answers for x into the equation below to get the answers which should both be .25<BR>\n" );
document.write( "100x/(3x^2 + 103x + 3)<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Ed\r<BR>\n" );
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document.write( " </SPAN>\n" );
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