SOLUTION: Simplify: (y-z)/yz - (z-x)/zx - (x-y)/xy This posted answer is 2(y-z)/yz But I don't know how this was arrived at. I keep getting 0/yzx Appreciate any help.

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Question 234462: Simplify:
(y-z)/yz - (z-x)/zx - (x-y)/xy
This posted answer is 2(y-z)/yz
But I don't know how this was arrived at.
I keep getting 0/yzx
Appreciate any help.
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
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:

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

and these terms added together:

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

and these terms canceled out:

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