document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1119299>Question 1119299</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Variable in the Radicand?\r<BR>\n" );
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document.write( "I've been staring at this for just about an hour now, and for some reason my brain just won't process it. I'd love some help on this! \r<BR>\n" );
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document.write( "Look at the following expression. Are there any values of x for which the expression is not defined under the set of real numbers? Explain your reasoning. <BR>\n" );
document.write( "4/ square root of (x+2) \r<BR>\n" );
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document.write( "Rewrite the following expression by rationalizing the denominator. <BR>\n" );
document.write( "4/ square root of (x+2) <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 #734789 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=734789\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "Expressions with zero denominators do not exist (DNE).  In other words, they do not represent any real number. Expressions with radicands (expressions under a radical sign) that are less than zero are complex numbers and are not included in the set of real numbers. Hence, in order for the given expression to represent a real value, you must exclude values for <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\"> that are the elements of the set:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \{x\ \in\ \mathbb{R}\ |\ x\ +\ 2\ \leq\ 0\}\">\r<BR>\n" );
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document.write( "Which is to say:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \{x\ \in\ \mathbb{R}\ |\ x\ \leq\ -2\}\">\r<BR>\n" );
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document.write( "To rationalize the denominator in an expression of the form <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \frac{a}{\sqrt{b}}\">, multiply the fraction by 1 in the form of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \frac{\sqrt{b}}{\sqrt{b}}\">, thus:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \(\frac{a}{\sqrt{b}}\)\(\frac{\sqrt{b}}{\sqrt{b}}\)\ =\ \frac{a\sqrt{b}}{b}\"><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" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \ \\r\"> </SPAN>\n" );
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