document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=181648>Question 181648</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0321233832/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> 3x/9x-15\r<BR>\n" );
document.write( "\n" );
document.write( "This is what I did<BR>\n" );
document.write( "3x/9x-15<BR>\n" );
document.write( "1x/3x-15<BR>\n" );
document.write( "1/3-15=-44/3 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #136280 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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/cgi-bin/show-face.mpl?user=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=136280\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "You <i><b>might</b></i> be correct.  It all depends on what you meant by 3x/9x-15.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "If you meant:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \text{          }\math \frac{3x}{9x} - 15\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Then you are absolutely correct.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "On the other hand, if you meant:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \text{          }\math \frac{3x}{9x-15}\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Then you have a bit of a problem with your process.  You cannot separate the terms in a polynomial numerator or denominator and then operate with the separated terms individually.  Let me demonstrate on this problem with a couple of simple substitutions:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Let <i>x</i> = 1, then \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \text{          }\math \frac{3(1)}{9(1)- 15}  = \frac {3}{-6} = -\frac {1}{2} \neq -\frac {44}{3}\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "or let <i>x</i> = 2, then \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \text{          }\math \frac{3(2)}{9(2)- 15}  = \frac {6}{3} = 2\neq -\frac {44}{3}\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "What you can do with this problem is factor out the 3 that is common to both the numerator and both terms of the denominator and then eliminate it, thus:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \text{          }\math \frac{3(x)}{3(3x-5)} = \left(\frac{3}{3}\right)\left(\frac{x}{3x-5}\right) = 1 \ast \left( \frac{x}{3x-5} \right) = \frac{x}{3x-5}\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "And that is as much as you can do with this expression, except to make sure you restrict the value of <i>x</i> such that <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x \neq \frac {5}{3}\"> because that value would make the denominator equal 0.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
document.write( "</font> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );