Rearranging an equation and drawing a blank

[samsquaunch]

I need to rearrange this equation to solve for b but I can not get it worked out to where my units end up being correct.

(a-b)=(F*b)/(A*E)

 

[fresh_42]

I need to rearrange this equation to solve for b but I can not get it worked out to where my units end up being correct.

(a-b)=(F*b)/(A*E)

Can you retype it with units? Where's your difficulty?

 

[samsquaunch]

I end up with b=(AEa)/(F+AE) but A=mm^2 E=N/mm^2 a=mm F=N and b needs to be mm but I am left with the N from F with nothing to cancel it out.

 

[fresh_42]

I end up with b=(AEa)/(F+AE) but A=mm^2 E=N/mm^2 a=mm F=N and b needs to be mm but I am left with the N from F with nothing to cancel it out.

$unit(b) = \frac{unit(AEa)}{unit(F+AE)}= \frac{unit(A)unit(E)unit(a)}{unit(F)+unit(A)unit(E)}= \frac{mm^2 \cdot \frac{N}{mm^2} \cdot mm}{N + mm^2 \cdot \frac{N}{mm^2}} = \frac{N \cdot mm}{N} = mm$

 

[samsquaunch]

I don't understand why the N is still on top. Doesn't A and E both cancel each other out so that all that remains is F and a?

 

[fresh_42]

I don't understand why the N is still on top. Doesn't A and E both cancel each other out so that all that remains is F and a?

What do you mean by "cancel each other out"? $unit (A\cdot E) = unit(A) \cdot unit (E) = mm^2 \cdot \frac{N}{mm^2} = N$.

If you divide by $AE$ first then you'll have $b = \frac{a}{\frac{F}{AE} + 1}$ and therefore $$unit(b) = \frac{unit(a)}{\frac{unit(F)}{unit(AE)}+unit(1)} = \frac{mm}{\frac{N}{mm^2 \cdot \frac{N}{mm^2}}+0} = \frac{mm}{\frac{N}{N}} = \frac{mm}{1} = mm$$.

 

[samsquaunch]

Alright thank you that just finally made it sink in. I was looking at it if there is an AE on the top and bottom they would just cancel each other out but the way you laid it out here makes a lot of sense.