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 ) *****
