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How can we calculate the derivative of function f(x)= (x+2)/(x-1)?

In order to calculate the derivative of the given function, we need to apply the laws of derivation. Therefore:

f '(x) = ((x+2)/(x-1))'

f '(x) = [(x+2)' * (x-1) - (x+2) * (x-1)' ]/ (x-1)2

f '(x) = [ 1 * (x-1) - (x+2) * 1] / (x-1)2

f '(x) = x-1-x-2 / (x-1)2

f '(x) = -3 / (x-1)2

Therefore, we have calculated the derivative of the given function.

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