document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=950938>Question 950938</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me figure this out.<BR>\n" );
document.write( "f(x) = (1-x)/5x,   g(x) = 1/(1+5x)<BR>\n" );
document.write( "I am solving for g(f(x)) and f(g(x))<BR>\n" );
document.write( "I started and got confused with the denominator and can't seem to reduce the denominator properly.  I started with f(g(x)) and got (1-(1/1+5x) / 5(1/(1+5x) and am totally confused.  Could someone please explain how to do this?   </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #580688 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=580688\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> f(x) = (1-x)/5x, g(x) = 1/(1+5x)<BR>\n" );
document.write( " I am solving for g(f(x)) and f(g(x))<BR>\n" );
document.write( "------<BR>\n" );
document.write( "g[f(x)] = g[(1-x)/5x] = 1/[1 + 5[(1-x)/5x]]<BR>\n" );
document.write( "------<BR>\n" );
document.write( "= 1/[1+(1-x)/x]<BR>\n" );
document.write( "------<BR>\n" );
document.write( "= 1/[x + 1-x]/x<BR>\n" );
document.write( "------<BR>\n" );
document.write( "= 1/(1/x)<BR>\n" );
document.write( "====<BR>\n" );
document.write( "= x<BR>\n" );
document.write( "------------------------------<BR>\n" );
document.write( "Note:: f(x) = [1/5x]-[1/5]<BR>\n" );
document.write( "----------------------<BR>\n" );
document.write( "f[g(x)] = f[1/(1+5x)] = [1/[5[1/(1+5x)]-[1/5]<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "= [1/[5/(1+5x)] - [1/5)<BR>\n" );
document.write( "= [(1+5x)/5] - [1/5]<BR>\n" );
document.write( "= [1+5x-1]/5<BR>\n" );
document.write( "= 5x/5<BR>\n" );
document.write( "= x<BR>\n" );
document.write( "===============<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( "-----------------<BR>\n" );
document.write( "  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );