Homework Help

Solve this formula for R.  Simplify your answer. 1/R = 1/a+1/b Use parenthesis around...

user profile pic

kristenmarieb... | Student, Grade 10 | Valedictorian

Posted April 5, 2013 at 3:29 AM via web

dislike 2 like

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

user profile pic

violy | High School Teacher | (Level 3) Assistant Educator

Posted April 5, 2013 at 3:36 AM (Answer #1)

dislike 2 like

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).

 

user profile pic

pramodpandey | College Teacher | Valedictorian

Posted April 5, 2013 at 4:57 AM (Answer #3)

dislike 1 like

`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)`

user profile pic

paduncan | High School Teacher | (Level 1) Adjunct Educator

Posted April 5, 2013 at 4:30 AM (Answer #2)

dislike 0 like

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

 

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes