Question 234462
Original equation is:


(y-z)/yz - (z-x)/zx - (x-y)/xy


Multiply numerator and denominator by (yz*zx*xy) to get:


(yz*zx*xy)*(y-z)/yz)  - (yz*zx*xy)*(z-x)/zx) - (yz*zx*xy)*x-y)/xy)


This becomes:


( (zx*xy)*(y-z) - (yz*xy)*(z-x) - (yz*zx)*x-y) ) / (yz*zx*xy)


This is equivalent to:


( x^2yz * (y-z) - xy^2z * (z-x) - xyz^2 * (x-y) ) / (x^2y^2z^2)


Simplify by multiplying out all the factors to get:


( x^2y^2z - x^2yz^2 - xy^2z^2 + x^2y^2z - x^2yz^2 + xy^2z^2 ) / (x^2y^2z^2) *****


Combine like terms to get:


(2x^2y^2z - 2x^2yz^2) / (x^2y^2z^2)


Factor the numerator to get:


2x^2yz * (y - z) / (x^2y^2z^2)


x^2 in numerator and denominator cancel out.
y in numerator and y^2 in denominator become y in denominator
z in numerator and z^2 in denominator become z in denominator.


You are left with:


2(y - z) / yz


It's a real eyesore.


Putting the x and y and z in order helps to see it as I did above.


Also the signs might very easily have thrown you off.


The numerator above before combining like terms was:


( x^2y^2z - x^2yz^2 - xy^2z^2 + x^2y^2z - x^2yz^2 + xy^2z^2 ) *****



These terms added together:


( <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 ) *****


and these terms added together:


( 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 ) *****


and these terms canceled out:


( 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> ) *****