document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=40707>Question 40707</A>: <I><SPAN STYLE=\"word-break: break-all;\"> simplify:\r<BR>\n" );
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document.write( "y-z/a+b  times  a^2-b^2/z-y\r<BR>\n" );
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document.write( "please do it step by step so I understand it </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #26140 by </B><A HREF=/tutors/aboutme.mpl?userid=junior403><B>junior403(76)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=junior403><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=26140\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Simplify.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28y-z%29%2F%28a%2Bb%29%29%2A%28%28a%5E2-b%5E2%29%2F%28z-y%29%29 ALIGN=MIDDLE  ALT=\"%28%28y-z%29%2F%28a%2Bb%29%29%2A%28%28a%5E2-b%5E2%29%2F%28z-y%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "First we need to simplify by factoring in order to cancel these expressions.<BR>\n" );
document.write( "The numerator in the fraction on the right is the difference of two squares.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2+-+b%5E2 ALIGN=MIDDLE  ALT=\"a%5E2+-+b%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "We can factor this as (a+b)(a-b)because if we FOIL these out we get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2+-+b%5E2 ALIGN=MIDDLE  ALT=\"a%5E2+-+b%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "In the denominator of the same fraction we can factor out a -1 in order to make the expression read (y-z) which is NOT the same as (z-y).<BR>\n" );
document.write( "So now we have...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28y-z%29%2F%28a%2Bb%29%29%2A%28%28a%2Bb%29%28a-b%29%2F-1%28y-z%29%29 ALIGN=MIDDLE  ALT=\"%28%28y-z%29%2F%28a%2Bb%29%29%2A%28%28a%2Bb%29%28a-b%29%2F-1%28y-z%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now we can cancel out all of our like terms.<BR>\n" );
document.write( "(y-z) in the numerator of the first expression can cancel with (y-z) in the denominator of the second expression.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%280%29%2F%28a%2Bb%29%29%2A%28%28a%2Bb%29%28a-b%29%2F-1%29 ALIGN=MIDDLE  ALT=\"%28%280%29%2F%28a%2Bb%29%29%2A%28%28a%2Bb%29%28a-b%29%2F-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(a+b)in the denominator of the first expression can cancel with (a+b) in the numerator of the second expression.<BR>\n" );
document.write( "Which becomes...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a-b%29%2F-1 ALIGN=MIDDLE  ALT=\"%28a-b%29%2F-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Or...<BR>\n" );
document.write( "-(a-b)<BR>\n" );
document.write( "or...<BR>\n" );
document.write( "(-a+b)<BR>\n" );
document.write( "or...<BR>\n" );
document.write( "(b-a)<BR>\n" );
document.write( "This is in its simplist form.<BR>\n" );
document.write( "I hope I explained this thoroughly enough for you.<BR>\n" );
document.write( "Good Luck!\r<BR>\n" );
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document.write( "  </SPAN>\n" );
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