h(t) = [itex]\sqrt{t - 1}[/itex](adsbygoogle = window.adsbygoogle || []).push({});

h(t + Δt) = [itex]\sqrt{t + Δt - 1}[/itex]

h(t + Δt) - h(t) = [itex]\sqrt{t + Δt - 1}[/itex] - [itex]\sqrt{t - 1}[/itex]

So far so good. This is where I get confused:

[itex]\frac{h(t + Δt) - h(t)}{Δt}[/itex] = [itex]\frac{1}{\sqrt{t + Δt - 1} - \sqrt{t - 1}

}[/itex]

I don't understand why dividing both sides by Δt allows for this statement to be true. Can someone explain this to me? It would be very much appreciated.

Thanks a lot.

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# Very basic question

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