Math Is Fun Forum

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Solve For a

Given R = 1/[(1/a) + (1/b)].

Let me see.

LCD for [(1/a) + (1/b)] is ab.

I get (b + a)/(ab).

R = (b + a)/(ab)

(ab)R = b + a

abR - a = b

a(bR - 1) = b

a = b/(bR - 1)

You say?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Solve For a

Here's a useful algebraic trick. It will help you to see if your working is right at each step. Choose values for a and b and work out what that makes R. Then use your values of R and b to see if the final value for a is the one you started with.

Normally I wouldn't choose the same for a as for b but your answer didn't look right. I needed a quick check.

I put a = b = 1/2 at the start and got R = 1.

R = 1 and b = 1/2 doesn't give a = 1/2.

I think it's the first R = where the trouble starts. That fraction is the wrong way up. But I think a new approach will get you to the answer more quickly.   Make 1/a the subject and when you've simplified to one fraction invert it for a.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Re: Solve For a

Here's a useful algebraic trick. It will help you to see if your working is right at each step. Choose values for a and b and work out what that makes R. Then use your values of R and b to see if the final value for a is the one you started with.

Normally I wouldn't choose the same for a as for b but your answer didn't look right. I needed a quick check.

I put a = b = 1/2 at the start and got R = 1.

R = 1 and b = 1/2 doesn't give a = 1/2.

I think it's the first R = where the trouble starts. That fraction is the wrong way up. But I think a new approach will get you to the answer more quickly.   Make 1/a the subject and when you've simplified to one fraction invert it for a.

Bob

Ok.