document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=815092>Question 815092</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi I've been trying to find out what to do and how to do and I'm stuck so I'm hoping you can help me <BR>\n" );
document.write( "Simplify the right-hand side of the equation <BR>\n" );
document.write( "What is f of x equal x square plus seven x plus ten over x square subtract seven x subtract eighteen \r<BR>\n" );
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document.write( "It looks like F(x) = x^2+7x+10<BR>\n" );
document.write( " ----------------------  x^2-7x-18<BR>\n" );
document.write( "And please show every step that will help so much thank you  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #490699 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39617)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=490699\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Are you asking for a simplification of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=F%28x%29=%28x%5E2%2B7x%2B10%29%2F%28x%5E2-7x-18%29 ALIGN=MIDDLE  ALT=\"F%28x%29=%28x%5E2%2B7x%2B10%29%2F%28x%5E2-7x-18%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ?\r<BR>\n" );
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document.write( "Factorize the numerator and denominator.  Look for common factors which are equivalent to a factor of 1.  Just be aware than if you cancel these, the meaning of the simplified form will be changed.\r<BR>\n" );
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document.write( "Numerator:  (x+2)(x+5)<BR>\n" );
document.write( "Denominator:  (x+2)(x-9)\r<BR>\n" );
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document.write( "The function can be rewritten, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=F%28x%29=%28%28x%2B2%29%28x%2B5%29%29%2F%28%28x%2B2%29%28x-9%29%29 ALIGN=MIDDLE  ALT=\"F%28x%29=%28%28x%2B2%29%28x%2B5%29%29%2F%28%28x%2B2%29%28x-9%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "BEFORE simplification, you must understand that the function has a skipped point at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-2 ALIGN=MIDDLE  ALT=\"x=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and an asymptote at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=9 ALIGN=MIDDLE  ALT=\"x=9\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "The simplification is to cancel the apparant <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B2%29%2F%28x%2B2%29 ALIGN=MIDDLE  ALT=\"%28x%2B2%29%2F%28x%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > as a factor of 1:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28h%28x%29=%28x%2B5%29%2F%28x-9%29%29 ALIGN=MIDDLE  ALT=\"highlight%28h%28x%29=%28x%2B5%29%2F%28x-9%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "You will note that I changed the name of this function.  The discontinuity at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-2 ALIGN=MIDDLE  ALT=\"x=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > is now gone, so the h(x) IS continuous there, but the asymptote at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=9 ALIGN=MIDDLE  ALT=\"x=9\"   DISABLED_style= \"max-width:90%; height:auto;\" > remains for h(x) as it does for F(x). </SPAN>\n" );
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