Intermediate algebra question, on finding and simplifying functions?

Question

For the function find and simplify for this equation.

f(x)=5/x

f(a+h) - f(a) / h

Don't even know where to begin with this question, can someone please walk me through the steps?

Answer 1

Just plug in what's in the parentheses, and then simplify.

f(a+h) = 5/(a+h)

f(a) = 5/a

So, this is what you've got:

5/(a+h) - (5/a)/h

5/(a+h) - 5/(ah)

Mulitply the first by (ah) and the second by (a+h) (to get a common denominator):

5(ah)/(ah*(a+h)) - (5*(a+h))/(ah*(a + h))

Combine the numerators:

(5ah - 5a - 5h)/(ah*(a + h))

5(ah - a - h)/(a²h + ah²)

Not sure how much more this could be simplified...

Answer 2

I think this is how you do it but I'm not sure.

for f(a+h)-f(a)/h just make it into this:

f(a+h) = f(a)/h , now from this you know a+h = x and f(a)/h = 5/x

That should get you started.