document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=360833>Question 360833</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi, I'm having some trouble with compositions of functions with fractions. <BR>\n" );
document.write( "Here is the question:<BR>\n" );
document.write( "f(x) = (x-1)/(x-3)<BR>\n" );
document.write( "g(x) = (x-8)/(x-9)\r<BR>\n" );
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document.write( "Find f(g(x))<BR>\n" );
document.write( "Find g(f(x))\r<BR>\n" );
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document.write( "Thank you SO much! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #257464 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=257464\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Computing f(g(x))\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=%28x-1%29%2F%28x-3%29 ALIGN=MIDDLE  ALT=\"f%28x%29=%28x-1%29%2F%28x-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28g%28x%29%29=%28g%28x%29-1%29%2F%28g%28x%29-3%29 ALIGN=MIDDLE  ALT=\"f%28g%28x%29%29=%28g%28x%29-1%29%2F%28g%28x%29-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=g%28x%29 ALIGN=MIDDLE  ALT=\"x=g%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > on the right side.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28g%28x%29%29=%28%28x-8%29%2F%28x-9%29-1%29%2F%28%28x-8%29%2F%28x-9%29-3%29 ALIGN=MIDDLE  ALT=\"f%28g%28x%29%29=%28%28x-8%29%2F%28x-9%29-1%29%2F%28%28x-8%29%2F%28x-9%29-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28x%29=%28x-8%29%2F%28x-9%29 ALIGN=MIDDLE  ALT=\"g%28x%29=%28x-8%29%2F%28x-9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28g%28x%29%29=%28x-8-%28x-9%29%29%2F%28x-8-3%28x-9%29%29 ALIGN=MIDDLE  ALT=\"f%28g%28x%29%29=%28x-8-%28x-9%29%29%2F%28x-8-3%28x-9%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply EVERY term by the LCD <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;\" > to clear out the fractions.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28g%28x%29%29=%28x-8-x%2B9%29%2F%28x-8-3x%2B27%29 ALIGN=MIDDLE  ALT=\"f%28g%28x%29%29=%28x-8-x%2B9%29%2F%28x-8-3x%2B27%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28g%28x%29%29=1%2F%28-2x%2B19%29 ALIGN=MIDDLE  ALT=\"f%28g%28x%29%29=1%2F%28-2x%2B19%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms.\r<BR>\n" );
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document.write( "I'll let you compute g(f(x)) </SPAN>\n" );
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