Solve the equation for the variable r. S=r/1-r?

Question

Solve the equation for the variable r.
S=r/1-r

I got Sr=r as the answer but I don't think that it is right.
Please explain to me how to solve it.

Thank you. =]

Answer 1

one way is:

s = r / (1-r)

if you multiply by 1-r you get

s(1-r)=r

s - sr = r

now add sr

s = r + sr

factor

s = r(1+s)

divide by 1+s

r = s/(1+s)

how simple is that?



although I would actually do it this way (see below) since it is easier to picture in my mind and do the whole thing in one step mentally, but I'll include the tedious steps to guide you along:



s = r / (1-r)

invert both sides

1/s = (1-r)/r = 1/r - 1

add 1

1+1/s = 1/r

combine fractions on the left

(s+1)/s = 1/r

invert both sides again

s/(s+1) = r

Answer 2

That's close actually. To solve the problem you have to multiply both sides by 1-r. That would give you r=s(1-r) if you need to solve it farther i think it would be r=s-sr but i'm not 100% on the second part.

Answer 3

S=r/1-r

multiply both sides by 1-r

r=S-Sr

Answer 4

use the cross rule first:

S/1=r/1-r --->S(1-r)=r --->S-Sr=r

set all the multiples of r to one side note that by moving them from one side to the other side sign changes:

S=r+Sr



Factor r in the right hand side:



S=r(1+S)

To find r u need to devide S by the 1+S

----> r=S/1+S

Answer 5

S = r/(1-r)

S-Sr=r

S=r+Sr

S=r(1+S)

r=S/(1+S)

Answer 6

S(1-r) = r

S - Sr = r

S = r + Sr

S = (1+S)r

S/(1+S) = r

Answer 7

Im not sure if this is right, but Im pretty sure it is....you have to do division first in the problem.. anything divided by one is always teh opposite number in this case letter so it would be r-r which would equal zero so.. S= 0..again not sure..

Answer 8

s = r/1-r

(1-r) s = r

s - rs = r

s = r + rs

s = r ( 1+s )

so, r = s/(1+s)

Answer 9

(1-r)(s)=r

s-sr=r

s-sr+sr=r+sr

s=r(1+s)

r=s/(1+s)