Simple algebra, derivations, integrations. Desperate need of help

[vice]

Simple algebra, derivations, integrations. Desperate need of help :)

Hi!
This is my first post here (and it's not a very funny one). :)

It's been a long time since I took any math, and I'm getting more and more confused. Need some help!

a'*m' = b'*m
a*m' = b*m

b-b'=(a-a')*(m/m')
(a-a')+(b-b')=(a-a')*(?)

What's supposed to fit where the question mark stands?

More stupid questions to come.

 

[Muzza]

Let us denote the questionmark with "x", so that we have:

(a - a') + (b - b') = (a - a') * x.

Divide both sides by (a - a'):

x = ((a - a') + (b - b')) / (a - a') = 1 + (b - b') / (a - a') ... (1)

But you knew that (b - b') = (a - a')(m/m'), i.e that (b - b')/(a - a') = (m/m'), so

x = 1 + m/m' ... (2)

Both (1) and (2) are possible answers.

 

[HallsofIvy]

You have b-b'=(a-a')*(m/m')

You go from b- b' to a-a'+ b- b' by adding a- a', of course. Doing that on both sides, you get a+ a'+ b- b'= a+ a'+ (a-a')(m/m')= (a-a')(1)+ (a-a')(m/m').

Now seeing that "(a- a')" in both parts on the right, you can factor it out:

a+ a'+ b- b'= (a-a')(1+ (m/m')).