document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=56862>Question 56862</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0534462162/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> verify that (2x+1)/x-1 is the inverse of x+1/x-2 . I only got to x= y+1/y-2 and got stuck on how to simplify.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #38608 by </B><A HREF=/tutors/aboutme.mpl?userid=Scriptor><B>Scriptor(36)</B></A><img src=\"/images/stars/stars-07.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Scriptor><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=38608\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Suppose f(x) = (2x+1)/(x-1) and g(x)= x+1/x-2\r<BR>\n" );
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document.write( "Now you have to check that f(g(x))= x  \r<BR>\n" );
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document.write( "Let's check this: \r<BR>\n" );
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document.write( "f(g(x)) = (2*g(x)+1)/(g(x)-1) \r<BR>\n" );
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document.write( "        = [2*(x+1/x-2) + 1]/(x+1/x-2 -1)\r<BR>\n" );
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document.write( "        = [2*(x+1/x-2)+(x-2/x-2]/[x+1/x-2)-(x-2/x-2)]\r<BR>\n" );
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document.write( "        = [(2x+2+x-2)/(x-2)] / [x+1-x+2/(x-2)]\r<BR>\n" );
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document.write( "        = 2x+2+x-x / x+1-x+2<BR>\n" );
document.write( "  <BR>\n" );
document.write( "        = x </SPAN>\n" );
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