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 May 10th, 2012, 02:34 PM #1 Senior Member   Joined: Feb 2011 Posts: 150 Thanks: 0 Simplifying an equation Hi, I'm doing a fluid dynamics problem and I need some help simplifying an equation I've ended up with. It's a big ask, but if someone would take the time to tell me what the simplest form of this would be it would be much appreciated. $$\frac{b}{2\lambda h-h}(h^2-\lambda ^2h^2)-\frac{-bh}{\lambda h-h}(h-\lambda h)-d(h-\lambda h)+\frac{d}{2h}(h^2-\lambda ^2h^2)$$ or if you prefer, the form $$\frac{b(h^2-\lambda ^2h^2)}{2\lambda h-h}-\frac{-bh(h-\lambda h)}{\lambda h-h}-d(h-\lambda h)+\frac{d(h^2-\lambda ^2h^2)}{2h}$$ Thanks very much. Jake
 May 10th, 2012, 03:12 PM #2 Global Moderator   Joined: May 2007 Posts: 6,835 Thanks: 733 Re: Simplifying an equation Three of the terms have h as a factor in both the numerator and denominator. You can start by cancelling them out. Also, (h - ?h) is a factor for all the terms and can be taken outside [ ].
 May 10th, 2012, 03:42 PM #3 Senior Member   Joined: Feb 2011 Posts: 150 Thanks: 0 Re: Simplifying an equation Thank you. Cancelling and bringing $$h-\lambda h$$ outside the bracket, I get: $$h-\lambda h\left [ \frac{b(1-\lambda h)}{2\lambda h} +\frac{b}{\lambda h}-d+\frac{d(1-\lambda h)}{2} \right ]$$ close?
May 10th, 2012, 08:35 PM   #4
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Re: Simplifying an equation

Quote:
 Originally Posted by jakeward123 $$\frac{b(c^2-a^2 c^2)}{2a c-c}-\frac{-bc(c-a c)}{a c-c}-d(c-a c)+\frac{d(c^2-a ^2c^2)}{2c}$$
[Changed (for myself) your h to c and your lambda to a; b and d remain same.]

The 2nd term's numerator can be written +bc(ac - c), so (ac - c) cancels out, and term becomes simply bc. Ok?

Before doing any more, can you make sure that 1st term's denominator is correctly shown:
like, could it be 2(ac - c)? Asking due to (ac - c) and (c - ac) being all over the place!

Anyhow, as it is, I got down to:
c(1 - a^2)(2b + dk) / (2k) + c(ad - b - d) where k = 2a - 1

It checks out ok: tested it.

May 11th, 2012, 12:37 PM   #5
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Re: Simplifying an equation

Quote:
 Originally Posted by jakeward123 Thank you. Cancelling and bringing $$h-\lambda h$$ outside the bracket, I get: $$h-\lambda h\left [ \frac{b(1-\lambda h)}{2\lambda h} +\frac{b}{\lambda h}-d+\frac{d(1-\lambda h)}{2} \right ]$$ close?
No! You were very sloppy! For example - second term: you have b/(?h), it should be b/(?-1).

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