document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=205516>Question 205516</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Question: The sum of the reciprocal of an integer and the reciprocal of six-more-than-that-integer is the same as 5 / 36.\r<BR>\n" );
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document.write( "I have no idea how to start to set this up or solve it.  I am so confused. <BR>\n" );
document.write( "Thank you for the help </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #155139 by </B><A HREF=/tutors/aboutme.mpl?userid=Targetweek><B>Targetweek(62)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Targetweek><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=155139\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2Fx%29%2B%281%2Fy%29+=+5%2F36 ALIGN=MIDDLE  ALT=\"%281%2Fx%29%2B%281%2Fy%29+=+5%2F36\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+x%2B6 ALIGN=MIDDLE  ALT=\"y+=+x%2B6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "now you have a systems of equations and can solve it<BR>\n" );
document.write( "first substitute the second equation into the first<BR>\n" );
document.write( "1.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2Fx%29%2B%281%2F%28x%2B6%29%29+=+5%2F36 ALIGN=MIDDLE  ALT=\"%281%2Fx%29%2B%281%2F%28x%2B6%29%29+=+5%2F36\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "2. Get the same denominator<BR>\n" );
document.write( "a. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2Fx%29%2B%28x%2Fx%29%281%2F%28x%2B6%29%29+=5%2F36 ALIGN=MIDDLE  ALT=\"%281%2Fx%29%2B%28x%2Fx%29%281%2F%28x%2B6%29%29+=5%2F36\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2Fx%29%2B%28x%2Fx%28x%2B6%29%29+=+5%2F36 ALIGN=MIDDLE  ALT=\"%281%2Fx%29%2B%28x%2Fx%28x%2B6%29%29+=+5%2F36\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "b. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x%2B6%29%2F%28x%2B6%29%29%281%2Fx%29%2B%28x%2Fx%28x%2B6%29%29+=+5%2F36 ALIGN=MIDDLE  ALT=\"%28%28x%2B6%29%2F%28x%2B6%29%29%281%2Fx%29%2B%28x%2Fx%28x%2B6%29%29+=+5%2F36\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B6%29%2Fx%28x%2B6%29%2Bx%2Fx%28x%2B6%29+=+5%2F36 ALIGN=MIDDLE  ALT=\"%28x%2B6%29%2Fx%28x%2B6%29%2Bx%2Fx%28x%2B6%29+=+5%2F36\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "3. Simplify by addiing together<BR>\n" );
document.write( "-> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x%2B6%29%2Fx%28x%2B6%29+=+5%2F36 ALIGN=MIDDLE  ALT=\"%282x%2B6%29%2Fx%28x%2B6%29+=+5%2F36\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "4. Simplify further<BR>\n" );
document.write( "a. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x%28x%2B6%29%29%2F1%29%28%282x%2B6%29%2Fx%28x%2B6%29%29+=+%28%28x%28x%2B6%29%29%2F1%29%285%2F36%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2B6+=+5x%28x%2B6%29%2F36 ALIGN=MIDDLE  ALT=\"2x%2B6+=+5x%28x%2B6%29%2F36\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "b. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2836%2F1%29%282x%2B6%29+=+%2836%2F1%29%285x%28x%2B6%29%2F36%29 ALIGN=MIDDLE  ALT=\"%2836%2F1%29%282x%2B6%29+=+%2836%2F1%29%285x%28x%2B6%29%2F36%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x%2B6%29%2F36+=+5x%28x%2B6%29 ALIGN=MIDDLE  ALT=\"%282x%2B6%29%2F36+=+5x%28x%2B6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "c. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2F36%2B6%2F36+=+5x%2Ax+%2B+5x%2A6 ALIGN=MIDDLE  ALT=\"2x%2F36%2B6%2F36+=+5x%2Ax+%2B+5x%2A6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F18%2B3%2F18+=+5x%5E2%2B30x ALIGN=MIDDLE  ALT=\"x%2F18%2B3%2F18+=+5x%5E2%2B30x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B3%29%2F18+=+5x%5E2%2B30x ALIGN=MIDDLE  ALT=\"%28x%2B3%29%2F18+=+5x%5E2%2B30x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "d. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2818%2F1%29%28%28x%2B3%29%2F18%29+=+%2818%2F1%29%285x%5E2%2B30x%29 ALIGN=MIDDLE  ALT=\"%2818%2F1%29%28%28x%2B3%29%2F18%29+=+%2818%2F1%29%285x%5E2%2B30x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B3+=+90x%5E2%2B540x ALIGN=MIDDLE  ALT=\"x%2B3+=+90x%5E2%2B540x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "5. Now get everything over to one side and simplify<BR>\n" );
document.write( "a. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=90x%5E2%2B539x-3+=+0 ALIGN=MIDDLE  ALT=\"90x%5E2%2B539x-3+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "6.Now use the quadratic formula to solve for x<BR>\n" );
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=90x%5E2%2B539x%2B-3+=+0 ALIGN=MIDDLE  ALT=\"90x%5E2%2B539x%2B-3+=+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=%28539%29%5E2-4%2A90%2A-3=291601 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28539%29%5E2-4%2A90%2A-3=291601\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=291601 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+=+%28-539%2B-sqrt%28+291601+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-539%2B-sqrt%28+291601+%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-%28539%29%2Bsqrt%28+291601+%29%29%2F2%5C90+=+0.0055606995840675 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28539%29%2Bsqrt%28+291601+%29%29%2F2%5C90+=+0.0055606995840675\"   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-%28539%29-sqrt%28+291601+%29%29%2F2%5C90+=+-5.99444958847296 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28539%29-sqrt%28+291601+%29%29%2F2%5C90+=+-5.99444958847296\"   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=90x%5E2%2B539x%2B-3 ALIGN=MIDDLE  ALT=\"90x%5E2%2B539x%2B-3\"   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=90x%5E2%2B539x%2B-3+=+90%28x-0.0055606995840675%29%2A%28x--5.99444958847296%29 ALIGN=MIDDLE  ALT=\"90x%5E2%2B539x%2B-3+=+90%28x-0.0055606995840675%29%2A%28x--5.99444958847296%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 0.0055606995840675, -5.99444958847296.\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+90%2Ax%5E2%2B539%2Ax%2B-3+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+90%2Ax%5E2%2B539%2Ax%2B-3+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
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document.write( "and there are your two answers\r<BR>\n" );
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document.write( "... actually it's not... those aren't integers... are you sure you input the problem verbatim </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );