document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=85127>Question 85127</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is the domain of f(x)= 6x+5/x+5 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #61350 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=61350\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Since we cannot divide by zero, we can find exclusions in the domain by setting the denominator equal to zero and solving for x:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B5=0 ALIGN=MIDDLE  ALT=\"x%2B5=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Set the denominator equal to zero\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-5 ALIGN=MIDDLE  ALT=\"x=-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Solve for x\r<BR>\n" );
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document.write( "Since x=-5 makes the denominator equal to zero, we must exclude -5 from our domain. So our domain is: x is the set of all real numbers, except x cannot equal -5. Basically we can choose any number we want, except -5, and plug it in for x to get a real number output.\r<BR>\n" );
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document.write( "In interval notation, the domain would look like this:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE (-\infty, -5 )\cup (-5,\infty)\"> where the \"U\" stands for union \r<BR>\n" );
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document.write( "Notice when we graph the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%286x%2B5%29%2F%28x%2B5%29 ALIGN=MIDDLE  ALT=\"y=%286x%2B5%29%2F%28x%2B5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > we get\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-10%2C+10%2C+-10%2C+10%2C+%286x%2B5%29%2F%28x%2B5%29%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-10%2C+10%2C+-10%2C+10%2C+%286x%2B5%29%2F%28x%2B5%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "and you can see that x=-5 is not part of the domain (note: the vertical line is not part of the graph, it is an asymptote)\r<BR>\n" );
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