help please with Solving for b: 1/t = 1/a + 1/b

[aquacat]

Solve for b. 1/t = 1/a + 1/b
I know the answer is b = at/a-t but I don't know how to show how I got there.

 

[Deleted member 4993]

Solve for b. 1/t = 1/a + 1/b
I know the answer is b = at/a-t but I don't know how to show how I got there.

1/t = 1/a + 1/b

1/b = 1/t - 1/a

continue....

 

[Bob Brown MSEE]

Solve for b. 1/t = 1/a + 1/b
I know the answer is b = at/a-t but I don't know how to show how I got there.

Sometimes it is easier to see the answer if you first get rid of all the fractions.
Multiply both sides by abt.

ab = bt + at
ab - bt = at
b(a-t) = at
etc.