document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=203523>Question 203523</A>: <I><SPAN STYLE=\"word-break: break-all;\"> simplify this expression:  (x-5)^3/|x-5|\r<BR>\n" );
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document.write( "I have the answer:(x-5)*|x-5|, but do not know how to get there </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #153546 by </B><A HREF=/tutors/aboutme.mpl?userid=jsmallt9><B>jsmallt9(3758)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jsmallt9><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=153546\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> One of the earliest lessons you learn about absolute value is that the absolute value of a positive number is that number. This is also true of the absolute value of 0. And finally the absolute value of a negative number is that number without its minus sign. Another way to express this is: The absolute value of a negative number is the negative of that negative number. Expressing these ideas in mathematical notation:<BR>\n" );
document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+%3E=+0 ALIGN=MIDDLE  ALT=\"a+%3E=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28a%29+=+a ALIGN=MIDDLE  ALT=\"abs%28a%29+=+a\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+%3C++0 ALIGN=MIDDLE  ALT=\"a+%3C++0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28a%29+=+-a ALIGN=MIDDLE  ALT=\"abs%28a%29+=+-a\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "We will use these to simplify: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-5%29%5E3%2Fabs%28x-5%29 ALIGN=MIDDLE  ALT=\"%28x-5%29%5E3%2Fabs%28x-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Case: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-5+%3E=+0 ALIGN=MIDDLE  ALT=\"x-5+%3E=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-5+%3E=+0 ALIGN=MIDDLE  ALT=\"x-5+%3E=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28x-5%29+=+x-5 ALIGN=MIDDLE  ALT=\"abs%28x-5%29+=+x-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > so your expression becomes:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-5%29%5E3%2F%28x-5%29 ALIGN=MIDDLE  ALT=\"%28x-5%29%5E3%2F%28x-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This simplifies to<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-5%29%5E2+=+%28x-5%29%28x-5%29 ALIGN=MIDDLE  ALT=\"%28x-5%29%5E2+=+%28x-5%29%28x-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Substituting <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28x-5%29 ALIGN=MIDDLE  ALT=\"abs%28x-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > in for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-5%29 ALIGN=MIDDLE  ALT=\"%28x-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > (Remember they are equal if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-5+%3E=+0 ALIGN=MIDDLE  ALT=\"x-5+%3E=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is true in this case):<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-5%29%2Aabs%28x-5%29 ALIGN=MIDDLE  ALT=\"%28x-5%29%2Aabs%28x-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Case: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+-+5+%3C+0 ALIGN=MIDDLE  ALT=\"x+-+5+%3C+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-5+%3C+0 ALIGN=MIDDLE  ALT=\"x-5+%3C+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28x-5%29+=+-%28x-5%29 ALIGN=MIDDLE  ALT=\"abs%28x-5%29+=+-%28x-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > so your expression becomes:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-5%29%5E3%2F%28-%28x-5%29%29 ALIGN=MIDDLE  ALT=\"%28x-5%29%5E3%2F%28-%28x-5%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This simplifies to<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%28x-5%29%5E2+=+-%28x-5%29%28x-5%29 ALIGN=MIDDLE  ALT=\"-%28x-5%29%5E2+=+-%28x-5%29%28x-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Substituting <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28x-5%29 ALIGN=MIDDLE  ALT=\"abs%28x-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > in for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%28x-5%29 ALIGN=MIDDLE  ALT=\"-%28x-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > (Remember they are equal if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-5+%3C+0 ALIGN=MIDDLE  ALT=\"x-5+%3C+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is true in this case):<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28x-5%29%2A%28x-5%29+=+%28x-5%29abs%28x-5%29 ALIGN=MIDDLE  ALT=\"abs%28x-5%29%2A%28x-5%29+=+%28x-5%29abs%28x-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "In either case we end up with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-5%29abs%28x-5%29 ALIGN=MIDDLE  ALT=\"%28x-5%29abs%28x-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. </SPAN>\n" );
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