Trying to understand rewritten equation

[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/(x₀+Δ_x - 1/x₀)) / Δ₀

can be rewritten as

Δf/Δx = 1/Δ_x (x₀-(x₀+Δ_x) / (x₀+Δ_x)x₀)

But I am not sure how this was done.

I hope someone can help me with this.

Thanks in advance.

Seán

 

[Mark44]

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/(x₀+Δ_x - 1/x₀)) / Δ₀

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.

can be rewritten as

Δf/Δx = 1/Δ_x (x₀-(x₀+Δ_x) / (x₀+Δ_x)x₀)

But I am not sure how this was done.

I hope someone can help me with this.

Thanks in advance.

Seán

 

[OnceMore]

Hello,

And thanks for the reply.

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-(x₀+Δ_x)

 

[Mark44]

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?

 

[Mark44]

Mod note: Moved from Precalc section.