# Thread: Given that y = (x-a)/(x+b), express in terms of a, b and y

1. ## Given that y = (x-a)/(x+b), express in terms of a, b and y

My working :

$\displaystyle y(x+b) = x-a$
$\displaystyle yx + yb = x-a$
$\displaystyle yx - x = -a - yb$
$\displaystyle x(y-1) = -a - yb$

Answer $\displaystyle x = (-a - yb)/(y-1)$

Do I need to further simplify?

Thanks for the help

2. ## Re: Given that y = (x-a)/(x+b), express in terms of a, b and y

Originally Posted by FailInMaths
Do I need to further simplify?
More elegant : $\displaystyle x=\frac{a+by}{1-y}$ or $\displaystyle x=-b+\frac{a+b}{1-y}$ (euclidean division).

3. ## Re: Given that y = (x-a)/(x+b), express in terms of a, b and y

Originally Posted by FernandoRevilla
More elegant : $\displaystyle x=\frac{a+by}{1-y}$ or $\displaystyle x=-b+\frac{a+b}{1-y}$ (euclidean division).
Hmm but is my answer mathematically correct above? I get confuse and messed up often when I move around with negative numbers

4. ## Re: Given that y = (x-a)/(x+b), express in terms of a, b and y

Originally Posted by FailInMaths
Hmm but is my answer mathematically correct above? I get confuse and messed up often when I move around with negative numbers