document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=295296>Question 295296</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am working on functions (fractions/ division) but I am stumped. Any help is appreciated.\r<BR>\n" );
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document.write( "compute and then simplify the quantity f (a + h) &#8722; f (a):\r<BR>\n" );
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document.write( "f(x)=2/x+1\r<BR>\n" );
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document.write( "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 #212837 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=212837\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First, let's compute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28a%2Bh%29 ALIGN=MIDDLE  ALT=\"f%28a%2Bh%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we do this by simply replacing each 'x' with 'a+h' and simplifying. So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28a%2Bh%29=2%2F%28a%2Bh%2B1%29 ALIGN=MIDDLE  ALT=\"f%28a%2Bh%29=2%2F%28a%2Bh%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Similarly, doing the same for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28a%29 ALIGN=MIDDLE  ALT=\"f%28a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > gets us <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28a%29=2%2F%28a%2B1%29 ALIGN=MIDDLE  ALT=\"f%28a%29=2%2F%28a%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "This then means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28a%2Bh%29-f%28a%29=2%2F%28a%2Bh%2B1%29-2%2F%28a%2B1%29 ALIGN=MIDDLE  ALT=\"f%28a%2Bh%29-f%28a%29=2%2F%28a%2Bh%2B1%29-2%2F%28a%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So the goal now is to simplify <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F%28a%2Bh%2B1%29-2%2F%28a%2B1%29 ALIGN=MIDDLE  ALT=\"2%2F%28a%2Bh%2B1%29-2%2F%28a%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Take note that the LCD is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%2Bh%2B1%29%28a%2B1%29 ALIGN=MIDDLE  ALT=\"%28a%2Bh%2B1%29%28a%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So multiply the first fraction by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%2B1%29%2F%28a%2B1%29 ALIGN=MIDDLE  ALT=\"%28a%2B1%29%2F%28a%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%28a%2B1%29%29%2F%28%28a%2Bh%2B1%29%28a%2B1%29%29-2%2F%28a%2B1%29 ALIGN=MIDDLE  ALT=\"%282%28a%2B1%29%29%2F%28%28a%2Bh%2B1%29%28a%2B1%29%29-2%2F%28a%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now multiply the second fraction by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%2Bh%2B1%29%2F%28a%2Bh%2B1%29 ALIGN=MIDDLE  ALT=\"%28a%2Bh%2B1%29%2F%28a%2Bh%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%28a%2B1%29%29%2F%28%28a%2Bh%2B1%29%28a%2B1%29%29-%282%28a%2Bh%2B1%29%29%2F%28%28a%2Bh%2B1%29%28a%2B1%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Combine the fractions: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%28a%2B1%29-2%28a%2Bh%2B1%29%29%2F%28%28a%2Bh%2B1%29%28a%2B1%29%29 ALIGN=MIDDLE  ALT=\"%282%28a%2B1%29-2%28a%2Bh%2B1%29%29%2F%28%28a%2Bh%2B1%29%28a%2B1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Distribute: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282a%2B2-2a-2h-2%29%2F%28%28a%2Bh%2B1%29%28a%2B1%29%29 ALIGN=MIDDLE  ALT=\"%282a%2B2-2a-2h-2%29%2F%28%28a%2Bh%2B1%29%28a%2B1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "And finally combine like terms: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-2h%29%2F%28%28a%2Bh%2B1%29%28a%2B1%29%29 ALIGN=MIDDLE  ALT=\"%28-2h%29%2F%28%28a%2Bh%2B1%29%28a%2B1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So in the end, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28a%2Bh%29-f%28a%29=%28-2h%29%2F%28%28a%2Bh%2B1%29%28a%2B1%29%29 ALIGN=MIDDLE  ALT=\"f%28a%2Bh%29-f%28a%29=%28-2h%29%2F%28%28a%2Bh%2B1%29%28a%2B1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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