SOLUTION: Find f(a), f(a+h), and then calculate and simplify (f(a+h)-f(a))/h f(x) = 3/x I could only get as far as this: f(a)=3/a f(a+h)=3/a+h (3/(a+h)-(3/a))/h then I thought that I

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Find f(a), f(a+h), and then calculate and simplify (f(a+h)-f(a))/h f(x) = 3/x I could only get as far as this: f(a)=3/a f(a+h)=3/a+h (3/(a+h)-(3/a))/h then I thought that I      Log On


   

Question 898780: Find f(a), f(a+h), and then calculate and simplify (f(a+h)-f(a))/h
f(x) = 3/x
I could only get as far as this:
f(a)=3/a
f(a+h)=3/a+h
(3/(a+h)-(3/a))/h
then I thought that I have to rule out h from the bottom but I could not figure out how to do that...
Found 2 solutions by Edwin McCravy, Theo:
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
%22f%28a%29%22%22%22=%22%223%2Fa
%22f%28a%2Bh%29%22%22%22=%22%223%2F%28a%2Bh%29
%22f%28a%2Bh%29%22-%22f%28a%29%22%22%22=%22%223%2F%28a%2Bh%29-3%2Fa
Before you go further and divide by h, get an LCD of a(a+h):

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%22f%28a%2Bh%29%22-%22f%28a%29%22%22%22=%22%22%283a-3%28a%2Bh%29%29%2F%28a%28a%2Bh%29%29

%22f%28a%2Bh%29%22-%22f%28a%29%22%22%22=%22%22%283a-3a-3h%29%2F%28a%28a%2Bh%29%29

%22f%28a%2Bh%29%22-%22f%28a%29%22%22%22=%22%22%28-3h%29%2F%28a%28a%2Bh%29%29

Now divide the left side by h and multiply the right side by 1%2Fh,
which is really doing the same thing to both sides:

%28%22f%28a%2Bh%29%22-%22f%28a%29%22%29%2Fh%22%22=%22%22expr%28%28-3h%29%2F%28a%28a%2Bh%29%29%29%2Aexpr%281%2Fh%29

%28%22f%28a%2Bh%29%22-%22f%28a%29%22%29%2Fh%22%22=%22%22expr%28%28-3cross%28h%29%29%2F%28a%28a%2Bh%29%29%29%2Aexpr%281%2Fcross%28h%29%29

%28%22f%28a%2Bh%29%22-%22f%28a%29%22%29%2Fh%22%22=%22%22-3%2F%28a%28a%2Bh%29%29

Edwin

Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
the steps are shown in the following picture.

steps 1, 2, and 3 are setting up the equations.

step 4 is where the action is.

you need to combine f(a+h) - f(a) in the numerator under a common denominator so you can perform the subtraction.

the common denominator is a*(a+h).

you are multiplying 3*(a+h) by (a/a)

you are multiplying 3/a by (a+h)/(a+h)

this gets the common denominator of a*(a+h) which allows you to combine the numerator under the common denominator.

you then simplify further to get:

(3a-3a-3h)/(a*(a+h)*h) which then simplifies to (-3h)/((a^2+h)*h)

once you've done that, you eliminate the h in the numerator and the denominator because they cancel each other out and you are left with (-3)/(a^2+h)

that's your solution.

you will eventually be taking the limit of that as h approaches 0 which will then get you the derivative of the original expression, but that's in the future.

for now, your solution is:

(-3)/(a^2+h)

$$$