document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1006237>Question 1006237</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The solution set in interval notation of the inequality (4/x-1)>(3/x) is:\r<BR>\n" );
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document.write( "A) (-&#8734;, 0)U(0, &#8734;)<BR>\n" );
document.write( "B) (-3, 0)U(1, &#8734;)<BR>\n" );
document.write( "C) (-&#8734;, -3)U(0, 1)<BR>\n" );
document.write( "D) (-&#8734;, -3)<BR>\n" );
document.write( "E) (0,1) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #622411 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39620)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=622411\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Ambiguous inequality, maybe really meant as 4/(x-1)>3/x,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2F%28x-1%29-3%2Fx%3E0 ALIGN=MIDDLE  ALT=\"4%2F%28x-1%29-3%2Fx%3E0\"   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=%284%2F%28x-1%29-3%2Fx%29%28x%28x-1%29%29%3E0%28x%28x-1%29%29 ALIGN=MIDDLE  ALT=\"%284%2F%28x-1%29-3%2Fx%29%28x%28x-1%29%29%3E0%28x%28x-1%29%29\"   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=4x-3%28x-1%29%3E0 ALIGN=MIDDLE  ALT=\"4x-3%28x-1%29%3E0\"   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=4x-3x%2B3%3E0 ALIGN=MIDDLE  ALT=\"4x-3x%2B3%3E0\"   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=x%2B3%3E0 ALIGN=MIDDLE  ALT=\"x%2B3%3E0\"   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=highlight%28x%3E-3%29 ALIGN=MIDDLE  ALT=\"highlight%28x%3E-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is the interval notation form,  (-3, infinity).<BR>\n" );
document.write( "Be aware, a critical value is x at 0.  The inequality will be UNDEFINED for x=0.<BR>\n" );
document.write( "Another critical value is x at 1; the inequality is UNDEFINED for x=1.\r<BR>\n" );
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document.write( "You will make better sense of the choices given if your inequality really is exactly as it was shown in your question:   <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2Fx-1%3E3%2Fx ALIGN=MIDDLE  ALT=\"4%2Fx-1%3E3%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and the only critical value would be x at 0 being the undefined value for x in the inequality.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2Fx-1-3%2Fx%3E0 ALIGN=MIDDLE  ALT=\"4%2Fx-1-3%2Fx%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fx-1%3E0 ALIGN=MIDDLE  ALT=\"1%2Fx-1%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1-1x%3E0 ALIGN=MIDDLE  ALT=\"1-1x%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1-x%3E0 ALIGN=MIDDLE  ALT=\"1-x%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Now the critical values of x are  0 and 1.<BR>\n" );
document.write( "The intervals on x to check are (-infinity,0), (0,1), and (1, infinity).\r<BR>\n" );
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document.write( "One should get all expressions onto one side with 0 on the other side before further simplifying because the denominators may be positive OR negative, affecting the order when performing the multiplication for the order relationship. </SPAN>\n" );
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