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.Com
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)   (Show Source): You can put this solution on YOUR website!



Before you go further and divide by h, get an LCD of a(a+h):









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







Edwin
Answer by Theo(13342)   (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)

$$$





RELATED QUESTIONS

if f(x)=x^2 - 7x, find f(a), f(a - 3), and f(a... (answered by richwmiller)
Suppose the function is f(x) = 3/x. Find and simplify f(a+h) - f(a). (answered by josgarithmetic)
find f(a), f(a+h), and f(a+h)-f(a)/h for... (answered by Fombitz)
Given f(x) = 2x² + 3x - 1 Find and simplify: {{{(f(a+h) - f(a))/h}}} (answered by josgarithmetic)
Suppose F(x) = 10 for all x Find F(0), F(-3) and... (answered by nerdybill)
Find f(a), f(a + h),and the difference quotient f(a + h) − f(a)/ h where h... (answered by Fombitz)
Find f(a), f(a + h), and the difference quotient f(a + h) − f(a)/h. where h... (answered by Alan3354,stanbon)
Find f(a), f(a+h), and the difference quotient f(a+h)-f(a)/h, where h is unequal to 0.... (answered by josgarithmetic)
f(x)= 3-4x Find... (answered by joyofmath)