document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=66390>Question 66390</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What values for X must be excluded in this fraction?\r<BR>\n" );
document.write( "\n" );
document.write( "x-3<BR>\n" );
document.write( "---------<BR>\n" );
document.write( "(4x-5)(x+1)\r<BR>\n" );
document.write( "\n" );
document.write( "How do I figure out the values to be excluded from this fraction? Thank you </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #47098 by </B><A HREF=/tutors/aboutme.mpl?userid=Earlsdon><B>Earlsdon(6294)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Earlsdon><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=47098\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The values of x that must be excluded are those values that would make the denominator equal zero.<BR>\n" );
document.write( "Why is that important?<BR>\n" );
document.write( "Because, in mathematics, division by zero is undefined! In other word it doesn't make sense, mathematically.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-3%29%2F%284x-5%29%28x%2B1%29 ALIGN=MIDDLE  ALT=\"%28x-3%29%2F%284x-5%29%28x%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So, in the denominator we have:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284x-5%29%2A%28x%2B1%29 ALIGN=MIDDLE  ALT=\"%284x-5%29%2A%28x%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Let's take these factors one-at-a-time.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x-5%29 ALIGN=MIDDLE  ALT=\"4x-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > To find the value of x that would make this equal zero, we just set this factor equal to zero and solve for x.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x-5+=+0 ALIGN=MIDDLE  ALT=\"4x-5+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add 5 to both sides.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x+=+5 ALIGN=MIDDLE  ALT=\"4x+=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now divide both sides by 4.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+5%2F4 ALIGN=MIDDLE  ALT=\"x+=+5%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > This is one of the excluded values of x! We can find the other one  by doing the same thing with the other factor.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B1+=+0 ALIGN=MIDDLE  ALT=\"x%2B1+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 1 from both sides.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-1 ALIGN=MIDDLE  ALT=\"x+=+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > This is the other excluded value of x. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );