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On this problem, we need to figure out what our F of X + H
is.
Well, whenever we have F of anything in the parenthesis, it
means that when we see our unknown, we're going to put in
whatever is in the parenthesis.
So our F of X + H is just 5 / X + H Our F of X is just 5 / X.
Now if that seems a little foreign, what I recommend is to
go back and do some numbers.
If I asked you for F of one, you would tell me 5 / 1 or five.
If I asked you for F of -7, you would say 5 / -7.
If I asked you for F of A, you would tell me 5 / A.
So if I ask you for F of X + H, hopefully you say 5 / X + H So
going back to the original problem, we now need to put in 5
/ X + H -, 5 / X all over H So our first step is to get a
common denominator, and that's going to be X * X + H for the
numerator of this complex fraction.
So we're going to have 5 * X minus.
Maybe I should do it in a few more steps.
5 * X and then we'll -5 * X + H over the X * X + H and that's
all divided by the H.
So if we distribute, we'd get five X -, 5 X -5 H over X * X +
H all divided by H The five XS are going to cancel, so we get
-5 H over X * X + H and if we divide by H, that's the really
the same thing as multiplying by 1 / H The HS are going to cancel
and we get -5 / X * X + H.