document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=277257>Question 277257</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Good evening guys. \r<BR>\n" );
document.write( "\n" );
document.write( "Here's my question.\r<BR>\n" );
document.write( "\n" );
document.write( "Simplify x+4  -  x-3<BR>\n" );
document.write( "            ____   ____<BR>\n" );
document.write( "             x-2      x+1<BR>\n" );
document.write( "            __________<BR>\n" );
document.write( "                   x+1\r<BR>\n" );
document.write( "\n" );
document.write( "I factored the equation\r<BR>\n" );
document.write( "\n" );
document.write( "(x+2)(x+2)     -     (x-1)(x+3)<BR>\n" );
document.write( "________            ________<BR>\n" );
document.write( "      x-2                     x+1<BR>\n" );
document.write( "_______________________<BR>\n" );
document.write( "                     x+1\r<BR>\n" );
document.write( "\n" );
document.write( "I cross cancelled the x+1 terms.\r<BR>\n" );
document.write( "\n" );
document.write( "And this I think is my new equation\r<BR>\n" );
document.write( "\n" );
document.write( "         (x+2)(x+2)     -    (x-3)<BR>\n" );
document.write( "          ________________<BR>\n" );
document.write( "                       x-2\r<BR>\n" );
document.write( "\n" );
document.write( "And then I'm not sure what to do except multiply the terms in the numerator and get<BR>\n" );
document.write( " 2(5x-1)<BR>\n" );
document.write( "______<BR>\n" );
document.write( "   x-2\r<BR>\n" );
document.write( "\n" );
document.write( "Any help is welcome. Thank you!                                                                   <BR>\n" );
document.write( "             </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #201914 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=201914\">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( "I think you are trying to say, at least in part, that the factors of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\ +\ 4\"> are <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\ +\ 2\"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\ +\ 2\">.  Tell you what -- I'll give you <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\ +\ 4\"> dollars and you give me <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large (x\ +\ 2)(x\ +\ 2)\ =\ x^2\ +\ 4x\ + 4\"> dollars in return so long as <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\ \geq\ 1\">.  So if <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\"> is 1, I give you 5 and you give me 9.  If <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\"> is  10, I give you 14 and you give me 144...\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Ok, now that we have debunked that theory, let's look at what we have:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{\frac{x+4}{x-2}\ -\ \frac{x-3}{x+1}}{x\ +\ 1}\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The first thing we need to do is combine the fractions in the numerator.  Since there are no common factors between the two denominators, the LCD is simply the product of the two denominators, namely:  <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large (x\ -\ 2)(x\ +\ 1)\">.  Applying the LCD we get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{\frac{(x+4)(x+1)-\left((x-3)(x-2)\right)}{(x-2)(x+1)}}{x\ +\ 1}\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Expand the three sets of binomials in the numerator using FOIL:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{\frac{(x^2\ +\ 5x\ +\ 4)-\left((x^2\ -\ 5x\ + 6)\right)}{(x^2\ -\ x\ -2)}}{x\ +\ 1}\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Remove the parentheses in the numerator of the numerator and collect like terms:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{\frac{x^2\ +\ 5x\ +\ 4\ -\ x^2\ +\ 5x\ -\ 6}{x^2\ -\ x\ -\ 2}}{x\ +\ 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{\frac{10x\ -\ 2}{x^2\ -\ x\ -\ 2}}{x\ +\ 1}\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Finally, take the <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\ +\ 1\"> denominator -- invert and multiply:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{10x\ -\ 2}{x^2\ -\ x\ -\ 2}\,\cdot\,\frac{1}{x\ +\ 1}\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{10x\ -\ 2}{x^3\ -\ 3x\ -\ 2}\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "And that is the best you can do with this one.\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" );