Differentiate y= (x-2)/(x^2-3)

Given y= (x-2) / (x^2 - 3)

We
need to find y'.

Since y is a quotient, then we will use
the quotient rule to find the derivative.

==> Let y=
u/v such that:

u= x-2   ==> u' =
1

v= x^2 -3  ==> v' =
2x

==> y' = (u'v-
uv')/v^2

==> y' = (1(x^2-3) - (x-2)(2x) ]/ (x^2
-3)^2

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

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

==> y' = -(x^2 -4x +3) / (x^2
-3)^2

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

==> y' = -(x-3)(x-1)/(x^2
-3)^2