# Solve this formula for R. Simplify your answer. 1/R = 1/a+1/b Use parenthesis around any polynomials in the numerator and/or denominator.

### 3 Answers | Add Yours

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)**.

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

`1/R=1/a+1/b`

`` Taking lcm on RHS.

`1/R=(b+a)/(ab)`

cross multiply

`ab=R(a+b)`

divide both side by (a+b)

`(ab)/(a+b)=R`

`R=(ab)/(a+b)`