document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1208025>Question 1208025</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given that f(x) = 1/x and (f/g)(x) = (x + 1)/(x^2 - x), find the function g. \r<BR>\n" );
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document.write( "Let me see.\r<BR>\n" );
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document.write( "I know that (f/x)(x) means f(x)/g(x). \r<BR>\n" );
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document.write( "I think the set up is this:\r<BR>\n" );
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document.write( "(1/x)/g(x) = (x + 1)/(x^2 - x)\r<BR>\n" );
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document.write( "I must find g(x).\r<BR>\n" );
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document.write( "You say?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #846144 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=846144\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "I'll denote f(x) as simply f. A similar story will apply for g as well.\r<BR>\n" );
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document.write( "f/g = (x+1)/(x^2-x)<BR>\n" );
document.write( "(1/x)/g = (x+1)/(x^2-x)<BR>\n" );
document.write( "1/(x*g) = (x+1)/(x(x-1))<BR>\n" );
document.write( "x*1/(x*g) = x*(x+1)/(x(x-1)) ..... multiply both sides by x.<BR>\n" );
document.write( "1/g = (x+1)/(x-1)<BR>\n" );
document.write( "<font color=red>g(x) = (x-1)/(x+1)</font> is the final answer.\r<BR>\n" );
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document.write( "Verification using WolframAlpha<BR>\n" );
document.write( "<a  rel=nofollow HREF=\"https://www.wolframalpha.com/input?i=f%28x%29%2Fg%28x%29+when+f%28x%29+%3D+1%2Fx+and+g%28x%29+%3D+%28x-1%29%2F%28x%2B1%29\">https://www.wolframalpha.com/input?i=f%28x%29%2Fg%28x%29+when+f%28x%29+%3D+1%2Fx+and+g%28x%29+%3D+%28x-1%29%2F%28x%2B1%29</a>\r<BR>\n" );
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document.write( "GeoGebra is another option.<BR>\n" );
document.write( "I recommend using the CAS tool in GeoGebra.<BR>\n" );
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