Help, Algebra II problem.?

Question

Can you please show steps :]

1/R= 1/r(sub1)+1/r(sub2) for r(sub2) the sub like exponent on bottom

the answer is r(sub2)=- r(sub1)R/R-r(sub1)

How do you get that? Help please :D

Answer 1

First, here's my convention: r(sub1) = (r1), r(sub2)= (r2)

1/R = 1/(r1) + 1/(r2)

1/(r2) = 1/R - 1/(r1)

Find a common denominator for the right side:

1/(r2) = (r1)/R(r1) - R/R(r1) = ((r1)-R)/R(r1)

Now take the reciprocal of both sides:

(r2) = (r1)R/((r1)-R) = -(r1)R/(R-(r1))

Answer 2

Your trying to get r2 so...

1/R-1/r(1) = 1/r(2)

now flip both sides of the equation

R-r(1) = r(2)...easy answer.   check your equation.  I think you left out a parenthesis on the right side. If this is the case.

The problem should have been

1/R = ( 1/r(1) + 1/r(2)  )

This would be done like this

1 = R* ( 1/r(1) + 1/r(2)  )

1 = ( R/r(1) + R/r(2)  )

1 -  R/r(1)  = R/r(2)

1/R - 1/r(1) = 1/r(2)

r(1)/( R*r(1) ) - R /( R*r(1) ) = 1/r(2)

(r(1)-R)/(R*r(1)) = 1/r(2)

(R*r(1)) / (r(1)-R) = r(2)

Remember if you ask questions on-line, change equation to use single variables, i.e.  a,b,c,r,z,...,x.  And remember parenthesis