document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=247216>Question 247216</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find the domain of each of the following rational functions.\r<BR>\n" );
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document.write( "2.)  f(x) = 5x+6<BR>\n" );
document.write( "            2x-6<BR>\n" );
document.write( "Simplify completely  (I don't understand this)<BR>\n" );
document.write( "6.)  -7xy^2<BR>\n" );
document.write( "      28x^2\r<BR>\n" );
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document.write( "16.)   x-2<BR>\n" );
document.write( "      8x^2-32<BR>\n" );
document.write( "    How do you put the line between the two sets of numbers?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #180390 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=180390\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Garamond\" size=\"+2\">\r<BR>\n" );
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document.write( "Like this:\r<BR>\n" );
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document.write( "You write:  f(x) = (5x+6)/(2x-6)  [The parentheses are essential]\r<BR>\n" );
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document.write( "I read that as\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ f(x)\ =\ \frac{5x\ +\ 6}{2x\ -\ 6}\">\r<BR>\n" );
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document.write( "The domain of a rational function is all real numbers EXCEPT any number that would make any denominator equal to 0.  So what number or numbers would make <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE 2x\ -\ 6\ = 0\">?\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{-7xy^2}{28x^2}\">\r<BR>\n" );
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document.write( "There is one factor of -1 in the numerator and none in the denominator, so the -1 stays put.\r<BR>\n" );
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document.write( "There is one factor of 7 in the numerator and one factor of 7 in the denominator because 28 equals 7 times 4.  So the 7 that is common to both numerator and denominator goes away, leaving you with a 4 in the denominator.\r<BR>\n" );
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document.write( "There is one factor of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x\"> in the numerator and two factors of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x\"> in the denominator.  The one factor that is common goes away and you are left with one factor of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x\"> in the denominator.\r<BR>\n" );
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document.write( "There are 2 factors of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE y\"> in the numerator and none in the denominator, so the 2 that are in the numerator stay put.\r<BR>\n" );
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document.write( "In summary, you have a factor of -1 and two factors of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE y\">, (which is to say, one factor of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE y^2\">) in the numerator.  You have one factor of 4 and one factor of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x\"> in the denominator.  Hence:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{-7xy^2}{28x^2}\ =\ \frac{-y^2}{4x}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{x\ -\ 2}{8x^2\ -\ 32}\">\r<BR>\n" );
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document.write( "The two terms in the denominator expression have a factor of 8 in common, so:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{x\ -\ 2}{8\left(x^2\ -\ 4\right)}\">\r<BR>\n" );
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document.write( "The binomial expression in the denominator is the difference of two squares.  Use the difference of two squares factorization:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ a^2\ -\ b^2\ =\ (a\ +\ b)(a\ -\ b)\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{x\ -\ 2}{8\left(x\ +\ 2\right)\left(x\ -\ 2\right)}\">\r<BR>\n" );
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document.write( "Now you can see that the numerator and denominator have a factor of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x\ -\ 2\"> in common.  Eliminate that factor from both numerator and denominator:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{1}{8\left(x\ +\ 2\right)}\">\r<BR>\n" );
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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" );
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