Simplifying/reducing a simple equation I have the following equation that I would like to simplify/reduce to a simpler form. 
Can anyone help me out solving this problem?
Thanks in advance for yout help!
$$z = -\frac{(1/n)-(1/y)}{(1/n)}$$
Or probably the correct way is:
$$z = -\frac{(\frac{1}{n})-(\frac{1}{y})}{(\frac{1}{n})}$$
Can this cut both $(1/n)$ to something like this:
$$z = (1/y)$$
 A: The "simplest form" of an equation is a matter of opinion, so maybe other people will tell you something else.
You have the equation
$$z = -\frac{\frac{1}{n} - \frac{1}{y}}{\frac{1}{n}}.$$
You can multiply both numerator and denominator of the fraction on the right-hand-side by $n$ to get
$$z = -\frac{n\cdot\frac{1}{n} - n\cdot\frac{1}{y}}{n\cdot\frac{1}{n}}.$$
Since $n\cdot\frac{1}{n} = 1$, this is the same as
$$z = -\frac{1-\frac{n}{y}}{1}.$$
Dividing by $1$ doesn't do anything, so I don't have to write it. The equation thus becomes
$$z = -\left(1-\frac{n}{y}\right).$$
Finally, I can clear the paranthesis on the right-hand-side, but since theres a minus sign in front of it, I need to flip the signs inside. I get:
$$z = -1+\frac{n}{y} = \frac{n}{y}-1,$$
where the last equality is just flipping the order of the terms. So $z = \frac{n}{y}-1$, which is much simpler than the original equation.
A: multiplying denominator and numerator by $$n$$ we get $$-(1-\frac{n}{y})$$
A: Distribute the negative sign and multiply by $\frac{n}{n}$ which is the same as multiplying by 1. This will give you $$z=\frac{n}{y} -1$$ 
A: The simplification can work in this way:
$$z = -\frac{(\frac{1}{n})-(\frac{1}{y})}{(\frac{1}{n})} =-\frac{(\frac{1}{n})}{(\frac{1}{n})}+\frac{(\frac{1}{y})}{(\frac{1}{n})} = -1+\frac{(\frac{1}{y})}{(\frac{1}{n})}=-1+\frac{n}{y}$$
