document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=60826>Question 60826</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0201746328/algebrahomeworkh>Intermediate Algebra 9th</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> FUNMATH- please help!!<BR>\n" );
document.write( "35. 4/x+3 + 7/x^2 - 3x + 9 = 108/x^3 + 27<BR>\n" );
document.write( "39. x-1/3 + 6x+1/15 + 2(x-2)/13-7x = 2(x+2)/5<BR>\n" );
document.write( "41. f(x) = 2x - 6/x; f(x) = 1<BR>\n" );
document.write( "45. f(x) = 6/x - 6/2x: f(x) = 5 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #41790 by </B><A HREF=/tutors/aboutme.mpl?userid=Nate><B>Nate(3500)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Nate><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=41790\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 4/(x + 3) + 7/(x^2 - 3x + 9) = 108/(x^3 + 27)<BR>\n" );
document.write( "4/(x + 3) + 7/(x^2 - 3x + 9) = 108/((x + 3)(x^2 - 3x + 9))<BR>\n" );
document.write( "4((x + 3)(x^2 - 3x + 9))/(x + 3) + 7((x + 3)(x^2 - 3x + 9))/(x^2 - 3x + 9) = 108((x + 3)(x^2 - 3x + 9))/((x + 3)(x^2 - 3x + 9))<BR>\n" );
document.write( "4(x^2 - 3x + 9) + 7(x + 3) = 108<BR>\n" );
document.write( "4x^2 - 12x + 36 + 7x + 21 = 108<BR>\n" );
document.write( "4x^2 - 6x - 51 = 0<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=4x%5E2%2B-6x%2B-51+=+0 ALIGN=MIDDLE  ALT=\"4x%5E2%2B-6x%2B-51+=+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=%28-6%29%5E2-4%2A4%2A-51=852 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-6%29%5E2-4%2A4%2A-51=852\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=852 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--6%2B-sqrt%28+852+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--6%2B-sqrt%28+852+%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-%28-6%29%2Bsqrt%28+852+%29%29%2F2%5C4+=+4.39862987983161 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-6%29%2Bsqrt%28+852+%29%29%2F2%5C4+=+4.39862987983161\"   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-%28-6%29-sqrt%28+852+%29%29%2F2%5C4+=+-2.89862987983161 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-6%29-sqrt%28+852+%29%29%2F2%5C4+=+-2.89862987983161\"   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=4x%5E2%2B-6x%2B-51 ALIGN=MIDDLE  ALT=\"4x%5E2%2B-6x%2B-51\"   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-6x%2B-51+=+4%28x-4.39862987983161%29%2A%28x--2.89862987983161%29 ALIGN=MIDDLE  ALT=\"4x%5E2%2B-6x%2B-51+=+4%28x-4.39862987983161%29%2A%28x--2.89862987983161%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 4.39862987983161, -2.89862987983161.\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-6%2Ax%2B-51+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+4%2Ax%5E2%2B-6%2Ax%2B-51+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-10%2C10%2C-10%2C10%2C4%2F%28x+%2B+3%29+%2B+7%2F%28x%5E2+-+3x+%2B+9%29%2C108%2F%28x%5E3+%2B+27%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "They are relatively the same. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );