How do I solve this algebra problem with unknown constant k?

[franky2727]

first of all forgive me for the writing of this as i don't have any programs to properly write it up, shouldn't be some hard for some of you wizz kids out there just don't see how to get from one line to the next to help would be much apprichiated (y - 1)/(y+2) = +or- ke^3/4x4 then the next line is y=(2Ke^3/4x4 +1)/1-Ke^3/4x4

where k is an unknown constant, thanks again in advance for a step by step guide through

 

[CompuChip]

If you write
$$\frac{y - 1}{y + 2} = \frac{y + 2 - 3}{y + 2} = \frac{y + 2}{y + 2} - \frac{3}{y + 2}$$
there's only one y left.

And don't worry, it's perfectly readable.

 

[franky2727]

dont i then get similar problems getting the y back with that 1 hanging arround, like when i multiply through? thanks for the help so far tho i can see where its going now just need another little push lol

 

[CompuChip]

You don't multiply through, you invert.
If you have
$$\frac{a}{b} = c = \frac{c}{1}$$
then also
$$\frac{b}{a} = \frac{1}{c}$$
(provided neither a nor c is zero).

Of course, c needn't be just a number, it could also be, say, $c = 1 + k e^{-3/4 x^4}$, if you get what I mean

 

[franky2727]

chears bud i owe u one dam resits doing my head in making enough at poker to earn like £100k a year but want a dam degree incase the industry goes tits up