document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=77159>Question 77159</A>: <I><SPAN STYLE=\"word-break: break-all;\"> what value for x must be excluded in the following fraction?\r<BR>\n" );
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document.write( "x-3<BR>\n" );
document.write( "over<BR>\n" );
document.write( "(4x-5)(x+1)<BR>\n" );
document.write( "am i right to say<BR>\n" );
document.write( "5/4,1,3 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #55451 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=55451\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-3%29%2F%28%284x-5%29%28x%2B1%29%29 ALIGN=MIDDLE  ALT=\"%28x-3%29%2F%28%284x-5%29%28x%2B1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "What values of x are not allowed?<BR>\n" );
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document.write( "The only thing that is not allowed in this expression is division by zero.  Therefore,<BR>\n" );
document.write( "neither of the two terms in the denominator can equal zero. You can solve for values<BR>\n" );
document.write( "of x that are not allowed by setting each of the factors in the denominator equal to zero<BR>\n" );
document.write( "and then solving for the corresponding value of x.<BR>\n" );
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document.write( "So begin by saying:<BR>\n" );
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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;\" ><BR>\n" );
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document.write( "Solve this by adding 5 to both sides to get <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;\" > and then dividing by the multiplier<BR>\n" );
document.write( "of x ... 4 ... to get that <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;\" >.  So you cannot let x equal <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F4 ALIGN=MIDDLE  ALT=\"5%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > because<BR>\n" );
document.write( "if it did, then the factor <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;\" > would equal zero. That one you got correctly.<BR>\n" );
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document.write( "Next do the same type of calculation for the other factor in the denominator <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B1 ALIGN=MIDDLE  ALT=\"x%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Set it equal to zero ...<BR>\n" );
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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;\" > and then subtract +1 from both sides to get <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 means that<BR>\n" );
document.write( "if you let x = -1, the factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%2B+1 ALIGN=MIDDLE  ALT=\"x+%2B+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > becomes zero and that would create a division<BR>\n" );
document.write( "by zero which is not an allowable situation in algebra. This one you called +1 ... <BR>\n" );
document.write( "suggesting that you probably made a sign error somewhere.<BR>\n" );
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document.write( "As far as the numerator going to zero ... that is not a problem. So you can solve the<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+-3+=+0 ALIGN=MIDDLE  ALT=\"x+-3+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and find that if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2B3 ALIGN=MIDDLE  ALT=\"x+=+%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" > the numerator goes to zero, but the factors in<BR>\n" );
document.write( "the denominator are not zero when x = +3. There is no division by zero that occurs when<BR>\n" );
document.write( "x = 3 ... and when x = 3 the two factors in the denominator are:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284x-5%29%2A%28x%2B1%29+=+%284%2A3+-+5%29%2A%283%2B1%29+=+%2812+-+5%29%2A%284%29+=+7%2A4+=+28 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > and since the numerator<BR>\n" );
document.write( "is zero when x = 3, the expression becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%2F28 ALIGN=MIDDLE  ALT=\"0%2F28\"   DISABLED_style= \"max-width:90%; height:auto;\" > and this is just zero ... which is OK.<BR>\n" );
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document.write( "In summary, the two non-allowed values are <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;\" > and <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;\" ><BR>\n" );
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document.write( "Hope this helps you to understand the problem a little more. </SPAN>\n" );
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