document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=234462>Question 234462</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Simplify:<BR>\n" );
document.write( "(y-z)/yz - (z-x)/zx - (x-y)/xy\r<BR>\n" );
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document.write( "This posted answer is 2(y-z)/yz<BR>\n" );
document.write( "But I don't know how this was arrived at.<BR>\n" );
document.write( "I keep getting 0/yzx   <BR>\n" );
document.write( "Appreciate any help. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #172914 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=172914\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Original equation is:\r<BR>\n" );
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document.write( "(y-z)/yz - (z-x)/zx - (x-y)/xy\r<BR>\n" );
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document.write( "Multiply numerator and denominator by (yz*zx*xy) to get:\r<BR>\n" );
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document.write( "(yz*zx*xy)*(y-z)/yz)  - (yz*zx*xy)*(z-x)/zx) - (yz*zx*xy)*x-y)/xy)\r<BR>\n" );
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document.write( "This becomes:\r<BR>\n" );
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document.write( "( (zx*xy)*(y-z) - (yz*xy)*(z-x) - (yz*zx)*x-y) ) / (yz*zx*xy)\r<BR>\n" );
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document.write( "This is equivalent to:\r<BR>\n" );
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document.write( "( x^2yz * (y-z) - xy^2z * (z-x) - xyz^2 * (x-y) ) / (x^2y^2z^2)\r<BR>\n" );
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document.write( "Simplify by multiplying out all the factors to get:\r<BR>\n" );
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document.write( "( x^2y^2z - x^2yz^2 - xy^2z^2 + x^2y^2z - x^2yz^2 + xy^2z^2 ) / (x^2y^2z^2) *****\r<BR>\n" );
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document.write( "Combine like terms to get:\r<BR>\n" );
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document.write( "(2x^2y^2z - 2x^2yz^2) / (x^2y^2z^2)\r<BR>\n" );
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document.write( "Factor the numerator to get:\r<BR>\n" );
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document.write( "2x^2yz * (y - z) / (x^2y^2z^2)\r<BR>\n" );
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document.write( "x^2 in numerator and denominator cancel out.<BR>\n" );
document.write( "y in numerator and y^2 in denominator become y in denominator<BR>\n" );
document.write( "z in numerator and z^2 in denominator become z in denominator.\r<BR>\n" );
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document.write( "You are left with:\r<BR>\n" );
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document.write( "2(y - z) / yz\r<BR>\n" );
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document.write( "It's a real eyesore.\r<BR>\n" );
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document.write( "Putting the x and y and z in order helps to see it as I did above.\r<BR>\n" );
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document.write( "Also the signs might very easily have thrown you off.\r<BR>\n" );
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document.write( "The numerator above before combining like terms was:\r<BR>\n" );
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document.write( "( x^2y^2z - x^2yz^2 - xy^2z^2 + x^2y^2z - x^2yz^2 + xy^2z^2 ) *****\r<BR>\n" );
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document.write( "These terms added together:\r<BR>\n" );
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document.write( "( <font size = \"6\"> x^2y^2z </font> - x^2yz^2 - xy^2z^2 <font size = \"6\"> + x^2y^2z </font> - x^2yz^2 + xy^2z^2 ) *****\r<BR>\n" );
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document.write( "and these terms added together:\r<BR>\n" );
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document.write( "( x^2y^2z <font size = \"6\"> - x^2yz^2 </font> - xy^2z^2 + x^2y^2z <font size = \"6\"> - x^2yz^2 </font> + xy^2z^2 ) *****\r<BR>\n" );
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document.write( "and these terms canceled out:\r<BR>\n" );
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document.write( "( x^2y^2z - x^2yz^2 <font size = \"6\"> - xy^2z^2 </font> + x^2y^2z - x^2yz^2 <font size = \"6\"> + xy^2z^2 </font> ) *****\r<BR>\n" );
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document.write( " </SPAN>\n" );
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