f(x)=[(x+∆x )+2/((x+∆x))]-[((x)+2/((x) )) ]

Two items:

1. Why do you have so many parentheses in this equation? It looks like what you mean is this:


f(x) = x + \Delta x + \frac x {(x + \Delta x)} - (x + \frac 2 x )


is that right?

2. Do you have a question?

You are right, to many parenthesis. Here is the correct the equation.

f(x)=[(x+∆x+2)/(x+∆x)]-[(x+2)/(x)]

OK great. That answers the first item I asked about. But how about the second - do you have a question?

Ok. My question is, what it would be the final result if I make the algebraic sustraction of the first function minus the second function.

First function: [(x+∆x+2)/(x+∆x)] MINUS (-) Second function: [(x+2)/(x)]

I get:


f(x) = \frac {-2 \Delta x} {x(x+ \Delta x)}


which for small values of \Delta x approaches:


f(x) = \frac {-2 \Delta x} {x^2}

Ok, great. And for the following one:

First function: [(x+∆x)+(2/(x+∆x))] MINUS (-) Second function: [x+(2/x)]

Thanks.