document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=147184>Question 147184</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find (f-g)(x). What is the domain of f/g\r<BR>\n" );
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document.write( "f(x)=2x-5  g(x)=2-x </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #107532 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=107532\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE (f-g)(x)=f(x)-g(x)\"> Start with the given property\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE f(x)-g(x)=\left(2x-5\right)-\left(2-x\right)\"> Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=2x-5 ALIGN=MIDDLE  ALT=\"f%28x%29=2x-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28x%29=2-x ALIGN=MIDDLE  ALT=\"g%28x%29=2-x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29-g%28x%29=2x-5-2%2Bx ALIGN=MIDDLE  ALT=\"f%28x%29-g%28x%29=2x-5-2%2Bx\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29-g%28x%29=3x-7 ALIGN=MIDDLE  ALT=\"f%28x%29-g%28x%29=3x-7\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE (\frac{f}{g})(x)=\frac{f(x)}{g(x)}\"> Start with the given property\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{f(x)}{g(x)}=\frac{2x-5}{2-x}\"> Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=2x-5 ALIGN=MIDDLE  ALT=\"f%28x%29=2x-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28x%29=2-x ALIGN=MIDDLE  ALT=\"g%28x%29=2-x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2-x=0 ALIGN=MIDDLE  ALT=\"2-x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Set the denominator equal to zero. Remember, dividing by 0 is undefined. So if we find values of x that make the denominator zero, then we must exclude them from the domain.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x=0-2 ALIGN=MIDDLE  ALT=\"-x=0-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >Subtract 2 from both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x=-2 ALIGN=MIDDLE  ALT=\"-x=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms on the right side\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-2%29%2F%28-1%29 ALIGN=MIDDLE  ALT=\"x=%28-2%29%2F%28-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by -1 to isolate x\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2 ALIGN=MIDDLE  ALT=\"x=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide\r<BR>\n" );
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document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2 ALIGN=MIDDLE  ALT=\"x=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > makes the denominator equal to zero, this means we must exclude <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2 ALIGN=MIDDLE  ALT=\"x=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > from our domain\r<BR>\n" );
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document.write( "So our domain is:  <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \textrm{\left{x|x\in\mathbb{R} x\neq2\right}}\">\r<BR>\n" );
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document.write( "which in plain English reads: x is the set of all real numbers except <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C%3E2 ALIGN=MIDDLE  ALT=\"x%3C%3E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So our domain looks like this in interval notation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \left(-\infty, 2\right)\cup\left(2,\infty \right)\">\r<BR>\n" );
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document.write( "note: remember, the parenthesis <font size=4><b>excludes</b></font> 2 from the domain\r<BR>\n" );
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document.write( "If we wanted to graph the domain on a number line, we would get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28500%2C50%2C-10%2C10%2C-10%2C10%2C%0D%0Anumber_line%28+500%2C+-8%2C+12%29%2C%0D%0Ablue%28arrow%280.2%2C-7%2C10%2C-7%29%29%2C%0D%0Ablue%28arrow%280.2%2C-6.5%2C10%2C-6.5%29%29%2C%0D%0Ablue%28arrow%280.2%2C-6%2C10%2C-6%29%29%2C%0D%0Ablue%28arrow%280.2%2C-5.5%2C10%2C-5.5%29%29%2C%0D%0Ablue%28arrow%280.2%2C-5%2C10%2C-5%29%29%2C%0D%0Ablue%28arrow%28-0.2%2C-7%2C-10%2C-7%29%29%2C%0D%0Ablue%28arrow%28-0.2%2C-6.5%2C-10%2C-6.5%29%29%2C%0D%0Ablue%28arrow%28-0.2%2C-6%2C-10%2C-6%29%29%2C%0D%0Ablue%28arrow%28-0.2%2C-5.5%2C-10%2C-5.5%29%29%2C%0D%0Ablue%28arrow%28-0.2%2C-5%2C-10%2C-5%29%29%2C%0D%0A%0D%0Acircle%280%2C-5.8%2C0.35%29%2C%0D%0Acircle%280%2C-5.8%2C0.4%29%2C%0D%0Acircle%280%2C-5.8%2C0.45%29%2C%0D%0Acircle%280%2C-5.8%2C0.4%29%2C%0D%0Acircle%280%2C-5.8%2C0.45%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Graph of the domain in blue and the excluded value represented by open circle\r<BR>\n" );
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document.write( "Notice we have a continuous line until we get to the hole at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2 ALIGN=MIDDLE  ALT=\"x=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > (which is represented by the open circle).<BR>\n" );
document.write( "This graphically represents our domain in which x can be any number except x cannot equal 2\r<BR>\n" );
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document.write( " </SPAN>\n" );
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