This is basic, I know, but it's been a long time since I've done equations. I'm watching a tutorial video on circuits.
Let's say I have this equation:
He then says "well we know all these V's are the same so we can divide both sides of that equation by V and we get 1 over R
Why does it become 1? I remember this kind of thing generally but not the specifics. What is this particular topic called so I can look it up and refresh on the subject?
On
Provided that $V\ne0$, we have: $$V=V$$ $$\to V=1\cdot V$$ $$\to \frac VV=\frac{1\cdot V}{V}$$ $$\to\frac VV=1$$
Hence your series of equations: $$\frac{V}{R_T}=\frac{V}{R_1}+\frac{V}{R_2}$$ becomes $$\frac{V}{V\cdot R_T}=\frac{V}{V\cdot R_1}+\frac{V}{V\cdot R_2}$$ $$\to\frac {1}{R_T}=\frac {1}{R_1}+\frac {1}{R_2}$$
Given$$\frac{V}{R_T}=\frac{V}{R_1}+\frac{V}{R_2}$$ $$V\left(\frac{1}{R_T}\right)=V\left(\frac{1}{R_1}+\frac{1}{R_2}\right)$$ Now cancel $V$ on both sides and we get $$\frac{1}{R_T}=\frac{1}{R_1}+\frac{1}{R_2}$$