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hala718 eNotes educator| Certified Educator

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

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