document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=264983>Question 264983</A>: <I><SPAN STYLE=\"word-break: break-all;\"> (x+1)/(x+3) = (x^2-11x)/(x^2+x-6) + (x-3)/(x-2) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #194948 by </B><A HREF=/tutors/aboutme.mpl?userid=JBarnum><B>JBarnum(2146)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=JBarnum><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=JBarnum><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=194948\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B1%29%2F%28x%2B3%29=%28%28x%5E2-11x%29%2F%28x%5E2%2Bx-6%29%29%2B%28x-3%29%2F%28x-2%29 ALIGN=MIDDLE  ALT=\"%28x%2B1%29%2F%28x%2B3%29=%28%28x%5E2-11x%29%2F%28x%5E2%2Bx-6%29%29%2B%28x-3%29%2F%28x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "must make the common denominator the same to add/subtract together<BR>\n" );
document.write( "just take your time and focus on just the denominators<BR>\n" );
document.write( "(x^2+x-6) , (x-2) , (x+3)<BR>\n" );
document.write( ".<BR>\n" );
document.write( "its common for books to provide the simpilar common denominator in the question.<BR>\n" );
document.write( "if you can factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2%2Bx-6%29 ALIGN=MIDDLE  ALT=\"%28x%5E2%2Bx-6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > it equals <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x-2%29%28x%2B3%29%29 ALIGN=MIDDLE  ALT=\"%28%28x-2%29%28x%2B3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "if you arent great at factoring  then first just try<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x-2%29%28x%2B3%29%29 ALIGN=MIDDLE  ALT=\"%28%28x-2%29%28x%2B3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to see if it = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2%2Bx-6%29 ALIGN=MIDDLE  ALT=\"%28x%5E2%2Bx-6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > since it is, you will multiply by the common denominator of<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x-2%29%28x%2B3%29%29 ALIGN=MIDDLE  ALT=\"%28%28x-2%29%28x%2B3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Now heres what it should look like:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x%2B1%29%2F%28x%2B3%29%29%28%28%28x-2%29%28x%2B3%29%29%2F1%29=%28%28%28x%5E2-11x%29%2F%28x%5E2%2Bx-6%29%29%28%28%28x-2%29%28x%2B3%29%29%2F1%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >+<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x-3%29%2F%28x-2%29%29%28%28%28x-2%29%28x%2B3%29%29%2F1%29%29 ALIGN=MIDDLE  ALT=\"%28%28x-3%29%2F%28x-2%29%29%28%28%28x-2%29%28x%2B3%29%29%2F1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now your ready to do cross cancelations and remember<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2%2Bx-6%29=%28%28x-2%29%28x%2B3%29%29 ALIGN=MIDDLE  ALT=\"%28x%5E2%2Bx-6%29=%28%28x-2%29%28x%2B3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x%2B1%29%28x-2%29%29=%28x%5E2-11x%29%2B%28%28x-3%29%28x%2B3%29%29 ALIGN=MIDDLE  ALT=\"%28%28x%2B1%29%28x-2%29%29=%28x%5E2-11x%29%2B%28%28x-3%29%28x%2B3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Use FOIL method (First Outer Inner Last)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2%2Bx-2x-2%29=%28x%5E2-11x%29%2B%28x%5E2-3x%2B3x-9%29 ALIGN=MIDDLE  ALT=\"%28x%5E2%2Bx-2x-2%29=%28x%5E2-11x%29%2B%28x%5E2-3x%2B3x-9%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%5E2-x-2=x%5E2-11x%2Bx%5E2-9 ALIGN=MIDDLE  ALT=\"x%5E2-x-2=x%5E2-11x%2Bx%5E2-9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2-x-2%29=%282x%5E2-11x-9%29 ALIGN=MIDDLE  ALT=\"%28x%5E2-x-2%29=%282x%5E2-11x-9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2-x-2%29-%28x%5E2-x-2%29=%282x%5E2-11x-9%29-%28x%5E2-x-2%29 ALIGN=MIDDLE  ALT=\"%28x%5E2-x-2%29-%28x%5E2-x-2%29=%282x%5E2-11x-9%29-%28x%5E2-x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=%282x%5E2-11x-9%29-%28x%5E2-x-2%29 ALIGN=MIDDLE  ALT=\"0=%282x%5E2-11x-9%29-%28x%5E2-x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=2x%5E2-11x-9-x%5E2%2Bx%2B2%29 ALIGN=MIDDLE  ALT=\"0=2x%5E2-11x-9-x%5E2%2Bx%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=x%5E2-10x-7%29 ALIGN=MIDDLE  ALT=\"0=x%5E2-10x-7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Use the Quadratic formula: Ax^2+Bx+C=0 where A=1 B=-10 C=-7<BR>\n" );
document.write( "the answer is: 10.6568542494924, -0.656854249492381<BR>\n" );
document.write( "<TABLE  BORDER=1>\n" );
document.write( "\n" );
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=1x%5E2%2B-10x%2B-7+=+0 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-10x%2B-7+=+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=%28-10%29%5E2-4%2A1%2A-7=128 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-10%29%5E2-4%2A1%2A-7=128\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=128 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--10%2B-sqrt%28+128+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--10%2B-sqrt%28+128+%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-%28-10%29%2Bsqrt%28+128+%29%29%2F2%5C1+=+10.6568542494924 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-10%29%2Bsqrt%28+128+%29%29%2F2%5C1+=+10.6568542494924\"   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-%28-10%29-sqrt%28+128+%29%29%2F2%5C1+=+-0.656854249492381 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-10%29-sqrt%28+128+%29%29%2F2%5C1+=+-0.656854249492381\"   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=1x%5E2%2B-10x%2B-7 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-10x%2B-7\"   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-10x%2B-7+=+1%28x-10.6568542494924%29%2A%28x--0.656854249492381%29 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-10x%2B-7+=+1%28x-10.6568542494924%29%2A%28x--0.656854249492381%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 10.6568542494924, -0.656854249492381.\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-10%2Ax%2B-7+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-10%2Ax%2B-7+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );