document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=159837>Question 159837</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The reciprocal of an integer plus the reciprocal of two times the integer plus two equals 2/3. Find the integer </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #117892 by </B><A HREF=/tutors/aboutme.mpl?userid=KnightOwlTutor><B>KnightOwlTutor(293)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KnightOwlTutor><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=KnightOwlTutor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=117892\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> X=unknown integer\r<BR>\n" );
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document.write( "1/X+1/2X+2=2/3\r<BR>\n" );
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document.write( "The common denominator for all is 3(X)(2X+2)\r<BR>\n" );
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document.write( "Multiply each term by the common denominator\r<BR>\n" );
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document.write( "3(2X+2)+3(X)=2(X)(2X+2)\r<BR>\n" );
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document.write( "use the distributive property\r<BR>\n" );
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document.write( "6X+6+3X=4x^2+4X<BR>\n" );
document.write( "9X+6=4X^2+4X\r<BR>\n" );
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document.write( "subtract 9X from each side\r<BR>\n" );
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document.write( "6=4X^2-5X\r<BR>\n" );
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document.write( "Subtract 6 from both sides<BR>\n" );
document.write( "0=4X^2-5X-6\r<BR>\n" );
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document.write( "This is a quadratic equation \r<BR>\n" );
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document.write( "Use the quadratic formula to solve<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=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=4x%5E2%2B-5x%2B-6+=+0 ALIGN=MIDDLE  ALT=\"4x%5E2%2B-5x%2B-6+=+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%2A4%2A-6=121 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-5%29%5E2-4%2A4%2A-6=121\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=121 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+121+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--5%2B-sqrt%28+121+%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+121+%29%29%2F2%5C4+=+2 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-5%29%2Bsqrt%28+121+%29%29%2F2%5C4+=+2\"   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+121+%29%29%2F2%5C4+=+-0.75 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-5%29-sqrt%28+121+%29%29%2F2%5C4+=+-0.75\"   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=4x%5E2%2B-5x%2B-6 ALIGN=MIDDLE  ALT=\"4x%5E2%2B-5x%2B-6\"   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=4x%5E2%2B-5x%2B-6+=+%28x-2%29%2A%28x--0.75%29 ALIGN=MIDDLE  ALT=\"4x%5E2%2B-5x%2B-6+=+%28x-2%29%2A%28x--0.75%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 2, -0.75.\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+4%2Ax%5E2%2B-5%2Ax%2B-6+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+4%2Ax%5E2%2B-5%2Ax%2B-6+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( "X=2\r<BR>\n" );
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document.write( "Plug in 2 for the variable x in the original equatio\r<BR>\n" );
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document.write( "1/2+(1/4+2)=2/3<BR>\n" );
document.write( "1/2+1/6+2/3\r<BR>\n" );
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document.write( "the common denominator is 6\r<BR>\n" );
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document.write( "3/6+1/6=4/6 simplify the term to 2/3 by dividing both numerator and denominator by 2\r<BR>\n" );
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document.write( " </SPAN>\n" );
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