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Multiply both sides by the LCD which is abR to get rid of the denominators.
`(abR)(1)/(R) = (abR)(1/a + 1/b) `
`(abR)/(R) = ((abR)/a + (abR)/b)`
Cancel out the common factor on top and bottom.
`ab = bR + aR`
Factor out R on right side.
`ab = R(b + a)`
Isolate the R on right side by dividing both sides by (b + a).
`(ab)/(b + a) = (R(b+a))/(b+a)`
Therefore, R = (ab)/(b + a) or R = (ab)/(a + b).
`` Taking lcm on RHS.
divide both side by (a+b)
1/R = 1/a +1/b
Common denominator is Rab
Multiply each term by common denominator Rab
ab = Rb + Ra
Use parentheses to simplify
ab = R(b+a)
Divide both sides of equation by (b+a) to solve for R
ab/(b+a) = R
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