How do I solve for b in the equation R = \frac{ab}{a+b}?

[thomas49th]

Homework Statement

Need to rearrange this equation to make b subject
$$R = \frac{ab}{a+b}$$



2. The attempt at a solution

R(a+b) = ab
Ra +Rb = ab
$$\frac{Rb}{b} = a$$ x -Ra


i think i did the last step wrong. Where do i go to now?

Thanks

 

[jing]

after Ra + Rb = ab

using addition and subtraction you need to get all terms that have a factor b on one side of the equation and all terms that do not have a factor of b on the other side of the equation

 

[thomas49th]

ive tried

$$\frac{Rb}{b} = a x -Ra$$

but i think that's wrong

can you show me what you'd do here?

 

[jing]

Yes it wrong. Go back to the step where you were correct (see my last post) and do not do any division at this stage. Have another read of my post and let me know if you do not understand what I am suggesting you do.

 

[thomas49th]

Ok

Ra + Rb = ab

can be written as

Ra + Rb = a x b

dont you cancel out x b with a /b (divide b)

If not, and you just use +/- then isn't it

Ra + Rb = ab
Rb - b = a - Ra
b(R-1) = a - Ra
b = a - Ra/(R-1)
But that doesn't look right to me...
Thanks

 

[cristo]

Ok

Ra + Rb = ab

can be written as

Ra + Rb = a x b

dont you cancel out x b with a /b (divide b)

If not, and you just use +/- then isn't it

Ra + Rb = ab
Rb - b = a - Ra
b(R-1) = a - Ra
b = a - Ra/(R-1)
But that doesn't look right to me...
Thanks

No, this is not right. You have: Ra+Rb=ab. Collect the terms including b together on one side: Ra=ab-Rb.

Now, can you factorise the right hand side? Once you have it factorised, it should be easy to make b the subject.

 

[jing]

Ok

If not, and you just use +/- then isn't it

Ra + Rb = ab
Rb - b = a - Ra
b(R-1) = a - Ra
b = a - Ra/(R-1)
But that doesn't look right to me...
Thanks

No you cannot separate the ab except by division

Ra + Rb = ab subtract Rb from both sides
Ra = ab -Rb factorise
Ra = b(a - R) now do the division to obtain b

 

[thomas49th]

Ra = ab - Rb
b(a-R) = Ra
b = Ra/(a - R)

 

[jing]

Yes it is right