I need help with this problem!

1. Sep 13, 2003

Learning

1/a+h+9 - 1/a+9 divide by h

This is a function and I suppose to calculate the value. But im stuck. Thanks for your help.

2. Sep 13, 2003

enigma

Staff Emeritus
Hi Learning, welcome to the forums!

Let me ask for clarification. You don't have any parenthesis, so the equation is a little ambiguous when looking at the screen.

Is this the equation:

1/(a+h+9) - (1/(a+9))/h

or is it something different?

3. Sep 13, 2003

Learning

Thats exactly right, sorry I forgot the those. Its different on the computer than writing it. Thanks

4. Sep 13, 2003

enigma

Staff Emeritus
Re: Re: I need help with this problem!

Ok,

Forum rules: you really should try the problem yourself first, so we can help where you got stuck. I can give you some pointers to get you started, though.

The trick is to get the h by itself on one side.

1/(a+h+9) - (1/(a+9))/h = 0

In this case, you'd first add (1/(a+9))/h to both sides, giving

1/(a+h+9) = (1/(a+9))/h

Then, multiply both sides by h, giving

h/(a+h+9) = 1/(a+9)

Give it a shot, and let us know how you do. Remeber, multiplying by X/X is the same as multiplying by 1.

5. Sep 14, 2003

Learning

Thanks for your help engima. Funny thing is thats where im stuck. I keep doing the problem that way, but I don't know where to go from there.

6. Sep 14, 2003

enigma

Staff Emeritus
Multiply both sides by the denominators, then add and subtract the h terms to one side, and all the others to the other side. Collect the coefficients on the h, and divide both sides by them.

Give it a shot, post your work!

7. Sep 14, 2003

Learning

I'm lost. Please work with me here.

8. Sep 16, 2003

HallsofIvy

Staff Emeritus
First, you will need to learn to be more precise: I noticed that when there was a question as to exactly what you meant, you apologized for not putting in parentheses to make it clear, but DIDN'T tell us what the correct formula was.

I assume that you mean, not 1/(a+h+9) - (1/(a+9))/h = 0, as enigma said (because there was no equation, initially) but rather,
(1/(a+h+9)- 1/(a+9))/h simply because that's a fairly standard "derivative" problem.

The first thing you should do is add the fractions: since they have different denominators, you need to get the same denominator by multiplying the numerator and denominator of the first fraction by (a+9): (a+9)/((a+h+9)(a+9)) and the numerator and denominator of the second fraction by (a+ h+ 9): (a+ h+9)/((a+h+9)(a+9))
(I did not multiply out the denominator because there is no need to.)

Now we know
1/(a+h+9)- 1/(a+9)= (a+9)/((a+h+9)(a+9))-(a+ h+9)/((a+h+9)(a+9))
= (a+9-(a+h+9))/((a+h+9)(a+9))
= -h/((a+h+9)(a+9))