Question

R(r^1+r^2) = r^1r^2, for r^2

Answer 1

hmm no one seems to like this one
ready?

Answer 2

Ready

Answer 3

\[R(r_1+r_2) = r_1r_2\]i am assuming they are subscripts right? not exponents

Answer 4

i am assuming that because no one writes \(r^1\) but you do see \(r_1\)

Answer 5

Oh yes I see the r1 not r^1 I'm sorry

Answer 6

in any case the first step is to multiply out on the left using the distributive law and get
\[Rr_1+Rr_2=r_1r_2\]

Answer 7

Okay

Answer 8

then lets put everything with an \(r_2\) in it on the left, and the other term on the right, via
\[Rr_2-r_1r_2=-Rr_1\] i did two steps at one, subtrcted \(r_1r_2\) from both sides and also subtracted \(Rr_1\) from both sides

Answer 9

is that step ok?

Answer 10

if not let me know and i can explain further
we have two more steps to go

Answer 11

Sure

Answer 12

ok now we want to get \(r_2\) by itself,so we have to factor it out of the expression on the left hand side. by the distributive law \(Rr_2-r_1r_2=(R-r_1)r_2\) we we can write
\[(R-r_1)r_2=-Rr_1\]

Answer 13

and finally to get \(r_2\) by itself we divide both sides by \(R-r_1\) to get
\[r_2=\frac{-Rr_1}{R-r_1}\]

Answer 14

or, if you prefer looking at fewer minus signs you would write this as
\[r_2=\frac{Rr_1}{r_1-R}\]

Answer 15

hope all steps are clear, i don't think i skipped any

Answer 16

Thank you you helped a lot :)