# Simplify factors

1. Nov 2, 2004

### danne89

Hi! I'm new to those forums, so I just want to say "Hello everbody!". To my question: How can I simplify $$\frac{\frac{1}{x+\Delta x}-\frac{1}{x}+ \frac{1}{x^2}\Delta x}{\Delta x}$$ I've spent some hours on google, but no result. Just tell me the name of the method and I'm really gratefull!

2. Nov 2, 2004

### Muzza

First simplify $\frac{1}{x+\Delta x}-\frac{1}{x}+ \frac{1}{x^2}\Delta x}$ by finding a common denominator.

3. Nov 2, 2004

### danne89

Hmm... Now I've $$\frac{x^2\Delta x}{x^3+x^2\Delta x}$$ for the nominator. Is that an inprovment?

Last edited: Nov 2, 2004
4. Nov 2, 2004

### Muzza

Well, yes, but I'm afraid it's wrong. This is very sloppily written (I've left out some parantheses), and h = delta x:

1/(x+h) - 1/x + h/x^2 =
x^2/x^2(x+h) - x(x + h)/x^2(x + h) + h(x + h)/(x + h)x^2 =
( x^2 - x(x + h) + h(x + h) ) / ((x + h)x^2) =
( x^2 - x^2 - xh + hx + h^2 ) / ((x + h)x^2) =
h^2 / ((x + h)x^2).

Upon division by h, we get

(1/(x+h) - 1/x + h/x^2) / h = h / ((x + h)x^2).

5. Nov 2, 2004

### danne89

Ah, nice. I think I got it now. Thanks!

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