Need help identifying which algebra rule was used

[LogarithmLuke]

https://www.physicsforums.com/threads/derivative-of-1-x.211489/

In the last post, three last steps. He changes -h into -1, how does this work? I know that if you for example have h/h it's equal to 1 regardless of what value h has, since they're both the same value. I don't see that being applied here though. Could anyone help me out?

By the way, i tried messaging the person who posted it, but he is no longer active on this forum. The thread is also not open for further replies.

 

[Mentallic]

If
$$f(x+h)-f(x)=\frac{-h}{x(x+h)}$$
then
$$\frac{f(x+h)-f(x)}{h}=\frac{-1}{x(x+h)}$$

Is this what you're asking about?

To simplify it, it's basically equivalent to

If
$$A = \frac{-h}{B}$$
then
$$\frac{A}{h}=\frac{-1}{B}$$
because
$$\frac{A}{h}=\frac{\left(\frac{-h}{B}\right)}{h}=\frac{-h}{Bh}=\frac{-1}{B}$$

But more simply, you can just notice that A has a factor of h in the numerator, so to divide A by h, you're then cancelling that factor.

 

[Doc Al]

In the last post, three last steps. He changes -h into -1, how does this work?

That's not what happened. What he did do was divide both sides by h.

 

[mathman]

What are you puzzled by? $\frac{-h}{h}=-1$

 

[LogarithmLuke]

I know, i just didn't think about the equation that was there, because that's not how i learned to do it in school. It didn't cross my mind that he used the fact that there was an equation there to move further with the math problem. When I've done these we never used equations, just simple factoring.

 

[Mark44]

I know, i just didn't think about the equation that was there, because that's not how i learned to do it in school. It didn't cross my mind that he used the fact that there was an equation there to move further with the math problem. When I've done these we never used equations, just simple factoring.

There's a big difference between simplifying an expression (such as by factoring and combining terms and so on) and working with an equation. When you're working with an expression, there are only a few things you can do, but when you're working with an equation, there are lots of things you can do: add the same expression to both sides, multiply both sides by the same value, divide both sides by the same nonzero value, take logs of both sides, and many others.