document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=200602>Question 200602</A>: <I><SPAN STYLE=\"word-break: break-all;\"> dap5654@aol.com. I am in intermediate algebra. I am having trouble with equations with rational expressions. <BR>\n" );
document.write( "Could you help me solve this equation? <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F3+=+4%2F%28x+%2B1%29 ALIGN=MIDDLE  ALT=\"x%2F3+=+4%2F%28x+%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >? I think the answer is 3,4. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #150852 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=150852\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Garamond\" size=\"+2\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "If you think the solution to an equation is a particular number, then the quickest way to make sure is to substitute that number back into the equation and see if you have a true statement.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "You think that one of the roots is 3:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{3}{3}\ =^?\ \frac{4}{3 + 1}\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{3}{3}\ = \frac{4}{4}\">.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "That one checks.  Now let's try 4:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{4}{3}\ =^?\ \frac{4}{4 + 1}\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{4}{3}\ \neq \frac{4}{5}\">.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Oops.  I guess we have to go back to the beginning.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{x}{3}\ = \frac{4}{x + 1}\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Step 1:  Cross multiply:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x(x + 1) = 12\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Step 2:  Standard form of the quadratic:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x^2 + x - 12 = 0\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Step 3:  Factor:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ -3 \times 4 = -12\"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE -3 + 4 = 1\">, so:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ (x - 3)(x + 4) = 0\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Step 4:  Zero Product Rule:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x - 3 = 0\ \ \Rightarrow\ \ x = 3\"> or\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x + 4 = 0\ \ \Rightarrow\ \ x = - 4\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "We have already checked 3, so lets try -4:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{-4}{3}\ =^?\ \frac{4}{-4 + 1}\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{-4}{3}\ = \frac{4}{-3}\">. Checks.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "What's the lesson?  Slow and steady, step by step.  And never stop at \"I think...\" You aren't done until you are sure.\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" );