document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=407624>Question 407624</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1/x + 1/(x+1) = 15/56 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #287308 by </B><A HREF=/tutors/aboutme.mpl?userid=graphmatics><B>graphmatics(170)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=graphmatics><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=graphmatics><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=287308\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1/x + 1/(x+1) = 15/56\r<BR>\n" );
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document.write( "multiply both sides by (x)*(x+1) and get<BR>\n" );
document.write( "1/x*(x*(x+1)) + (1/(x+1))*(x*(x+1)) = (15/56)*(x*(x+1))<BR>\n" );
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document.write( "(x+1) + x = (15/56)*(x^2 + x)<BR>\n" );
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document.write( "2*x + 1 = (15/56)*x^2 +(15/56)*x<BR>\n" );
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document.write( "-0.2678*x^2 -0.2678*x +2*x +1 = 0<BR>\n" );
document.write( "-0.2678*x^2 + 1.7321*x + 1 = 0\r<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=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=-0.2678x%5E2%2B1.7321x%2B1+=+0 ALIGN=MIDDLE  ALT=\"-0.2678x%5E2%2B1.7321x%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=%281.7321%29%5E2-4%2A-0.2678%2A1=4.07137041 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%281.7321%29%5E2-4%2A-0.2678%2A1=4.07137041\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=4.07137041 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+=+%28-1.7321%2B-sqrt%28+4.07137041+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-1.7321%2B-sqrt%28+4.07137041+%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-%281.7321%29%2Bsqrt%28+4.07137041+%29%29%2F2%5C-0.2678+=+-0.533352716778202 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%281.7321%29%2Bsqrt%28+4.07137041+%29%29%2F2%5C-0.2678+=+-0.533352716778202\"   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-%281.7321%29-sqrt%28+4.07137041+%29%29%2F2%5C-0.2678+=+7.00123919922779 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%281.7321%29-sqrt%28+4.07137041+%29%29%2F2%5C-0.2678+=+7.00123919922779\"   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=-0.2678x%5E2%2B1.7321x%2B1 ALIGN=MIDDLE  ALT=\"-0.2678x%5E2%2B1.7321x%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=-0.2678x%5E2%2B1.7321x%2B1+=+-0.2678%28x--0.533352716778202%29%2A%28x-7.00123919922779%29 ALIGN=MIDDLE  ALT=\"-0.2678x%5E2%2B1.7321x%2B1+=+-0.2678%28x--0.533352716778202%29%2A%28x-7.00123919922779%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: -0.533352716778202, 7.00123919922779.\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+-0.2678%2Ax%5E2%2B1.7321%2Ax%2B1+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-0.2678%2Ax%5E2%2B1.7321%2Ax%2B1+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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