Hi,
I need to rearrange this function in terms of z, I'm struggling a little bit (asterisks are multiplication):
a*(z-b) = -c*d*(f/(f+z))-(c*g)-h*e*(f/(f+z))-(h*i)
Any help?
I would start by mulitplying both sides through by $\displaystyle f+z$ . Then you have no nasty fractions. After this multiply out any brackets and then group terms of $\displaystyle z$ and $\displaystyle z^2$ together, what do you get?
Now that you're sober...OK, that's correct.
Problem/complication is, when multiplying through by f+z, we get az(f+z) = azf + az^2:
so we have a ye olde quadratic; going through with this mess, simplifying and combining, we'll get:
ax^2 + x(af - ab + cg + hi) + f(cd + cg + he + hi - ab) = 0 : recognize the quadratic?
Best way (for me anyway) to handle such a huge mudder is:
Let u = af - ab + cg + hi
Let v = f(cd + cg + he + hi - ab)
Then, using quadratic formula:
x = [-u +- SQRT(u^2 - 4av)] / (2a)
Any questions?!
What you think, Pickslide? You proud of me?