Trying to understand rewritten equation

1. May 2, 2012

OnceMore

Hello,

I am hoping someone can help me understand something. I was watching one of the MIT OCW videos and it ran through the following

Δf/Δx = (1/(x0x - 1/x0)) / Δ0

can be rewritten as

Δf/Δx = 1/Δx (x0-(x0x) / (x0x)x0)

But I am not sure how this was done.

I hope someone can help me with this.

Seán

2. May 2, 2012

Staff: Mentor

What you wrote above is very confusing. I believe that what you saw looked more like this:

Δf/Δx = (1/(x0+Δx) - 1/x0)) / Δx

Using LaTeX makes it even clearer.
$$Δf/Δx = \frac{\frac{1}{x_0 + Δx} - \frac{1}{x_0}}{Δx}$$

What is apparently happening is that they are finding the derivative of f(x) = 1/x, at the point x0.

The key to simplifying the above is being able to combine 1/(x0 + Δx) and 1/x0. To do this, find the common denominator and combine the two terms using that denominator.

3. May 2, 2012

OnceMore

Hello,

Yea, sorry about writing it like I did ..I am not too familiar with LaTeX.

Well, the common denominator is x0, which will give the x0-(x0x)

4. May 2, 2012

Staff: Mentor

No, the common denominator is NOT x0.

If you had to add 3/5 and 1/(5 + 3) would you say that the common denominator was 5?

5. May 2, 2012

Staff: Mentor

Mod note: Moved from Precalc section.

Last edited: May 2, 2012