(f(x+h)-f(x))/h when f(x)=1/(x+1)

(f(x + h) - f(x)) / h

when

f(x) = 1/(x+1)

f(x + h) = 1/(x + h + 1)

Now putting the values in the relation, we get

= (1/(x + h + 1) - 1/(x + 1)) / h

L.C.M is (x + 1)(x + h + 1). So

= [{(x + 1) - (x + h + 1)} / (x + 1)(x + h + 1)] / h

= (x + 1 - x - h - 1) / h(x + 1)(x + h + 1)

= - h / h(x + 1)(x + h + 1)

= - 1/(x + 1)(x + h + 1)

Hence

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