document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=468027>Question 468027</A>: <I><SPAN STYLE=\"word-break: break-all;\"> (x-7)/(x-8)-(x+1)/(x+8)+(x-24)/(x^2-64)\r<BR>\n" );
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document.write( "Perform the indicated operations and simplify? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #321119 by </B><A HREF=/tutors/aboutme.mpl?userid=ccs2011><B>ccs2011(207)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ccs2011><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/cgi-bin/show-face.mpl?user=ccs2011><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=321119\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x-7%29%2F%28x-8%29%29-%28%28x%2B1%29%2F%28x%2B8%29%29%2B%28%28x-24%29%2F%28x%5E2-64%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+64 ALIGN=MIDDLE  ALT=\"x%5E2+-+64\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This is an example of difference of squares<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-64+=+x%5E2+-+8%5E2+=+%28x-8%29%28x%2B8%29 ALIGN=MIDDLE  ALT=\"x%5E2+-64+=+x%5E2+-+8%5E2+=+%28x-8%29%28x%2B8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Next find common denominator<BR>\n" );
document.write( "*************<BR>\n" );
document.write( "Ex:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F4%29%2B%281%2F3%29%2B%281%2F12%29 ALIGN=MIDDLE  ALT=\"%281%2F4%29%2B%281%2F3%29%2B%281%2F12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The common denominator is the least common multiple of 3,4,12<BR>\n" );
document.write( "Since 3 and 4 are both factors of 12 then the LCM is 12.<BR>\n" );
document.write( "***********<BR>\n" );
document.write( "In the same way, (x-8) and (x+8) are factors of (x-8)(x+8)<BR>\n" );
document.write( "Thus the LCM and common denominator is (x-8)(x+8).<BR>\n" );
document.write( "However, the value of the expression cannot change, if the denominator changes then the numerator must change by the same factor.<BR>\n" );
document.write( "***************<BR>\n" );
document.write( "Ex:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F4%29%2B%281%2F3%29%2B%281%2F12%29+=+%283%2F12%29%2B%284%2F12%29%2B%281%2F12%29 ALIGN=MIDDLE  ALT=\"%281%2F4%29%2B%281%2F3%29%2B%281%2F12%29+=+%283%2F12%29%2B%284%2F12%29%2B%281%2F12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Because 4*3 = 12, multiply 1st fraction by 3, 2nd by 4, and 3rd by 1.<BR>\n" );
document.write( "**************<BR>\n" );
document.write( "In the same way, multiply 1st fraction by (x+8), 2nd by (x-8), 3rd by 1.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x%2B8%29%28x-7%29%2F%28x%2B8%29%28x-8%29%29-%28%28x-8%29%28x%2B1%29%2F%28x-8%29%28x%2B8%29%29%2B%28%28x-24%29%2F%28x-8%29%28x%2B8%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Since denominators are now the same, combine into one fraction<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x%2B8%29%28x-7%29+-+%28x-8%29%28x%2B1%29+%2B+%28x-24%29%29%2F%28%28x-8%29%28x%2B8%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Distribute on top and add like terms<BR>\n" );
document.write( "***************<BR>\n" );
document.write( "Note: <BR>\n" );
document.write( "(x+a)(x+b) = x^2 + (a+b)x + ab<BR>\n" );
document.write( "*****************<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x%5E2%2Bx-56%29+-+%28x%5E2-7x-8%29+%2B+%28x-24%29%29%2F%28%28x-8%29%28x%2B8%29%29 ALIGN=MIDDLE  ALT=\"%28%28x%5E2%2Bx-56%29+-+%28x%5E2-7x-8%29+%2B+%28x-24%29%29%2F%28%28x-8%29%28x%2B8%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "**Be careful when subtracting and remember to distribute the negative sign**<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2-x%5E2%2Bx%2B7x%2Bx-56%2B8-24%29%2F%28%28x-8%29%28x%2B8%29%29 ALIGN=MIDDLE  ALT=\"%28x%5E2-x%5E2%2Bx%2B7x%2Bx-56%2B8-24%29%2F%28%28x-8%29%28x%2B8%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%289x+-+72%29%2F%28%28x-8%29%28x%2B8%29%29 ALIGN=MIDDLE  ALT=\"%289x+-+72%29%2F%28%28x-8%29%28x%2B8%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Factor the 9 since it is a common factor to both 9 and 72<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%28x-8%29%2F%28%28x-8%29%28x%2B8%29%29 ALIGN=MIDDLE  ALT=\"9%28x-8%29%2F%28%28x-8%29%28x%2B8%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Cancel like factors both on top and bottom of a fraction<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-8%29%2F%28x-8%29+=+1 ALIGN=MIDDLE  ALT=\"%28x-8%29%2F%28x-8%29+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Therefore leaving the solution<BR>\n" );
document.write( "--> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%2F%28x%2B8%29 ALIGN=MIDDLE  ALT=\"9%2F%28x%2B8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );