Math Is Fun Forum

I was getting confused on a few steps. The * sign is confusing, you think of multiplication. It's subtle, you have to think forwards, then backwards.
But now I understand, well done.

You need to make clear your question by the use of brackets first, etc.
The first one you use the quotient rule.

y= (x-2) / (x-1)^2

so y(x) = u(x)/v(x)

then 

dy/dx = (v(du/dx) - u(dv/dx))/ v^2

or y' = (vu' - uv')/v^2

u = (x-2), v = (x-1)(x-1) = (x^2-2x+1) (we open up brackets to get to simple orders)

so, du/dx = 1, dv/dx = 2x-2

Therefore: dy/dx = ((x^2-2x+1)*1 - (x-2)*(2x-2))/ (x^2-2x+1)^2

= (x^2-2x+1)-2x^3+2x+4/(x^2-2x+1)^2

= (-2x^3 +x^2 + 5)/(x^2 - 2x +1)^2

= (-2x^3 +x^2  +5)/x^4 - 4x^3 +2x^2  - 4x +1

I could be very wrong though.

a +bd - (ab+ad) = ab + d - (ad + bd)
Let a = 1, b=2, d=3

7-5 = 5-9
2 = -4

So it's not associative?

Hmm, but the question was "show that (said operation) is associative" ???

Much appreciated Ricky, I know I've alot to learn, i'm just trying my best.

But how would I prove it?