How would I go about changing the subject of the formula 'y' = 'x' / 'a' - 'x' to 'x'?

Question

The formula is Y=X/A-X ('Y' equals 'X' divided by 'A' minus 'X')

How would I make the subject of the formula 'X'?

Answer 1

You need to get to a formula with X = .............

So I presume you mean Y = X / (A - X)

i) Multiply both sides by A-X :  AY-XY = X

ii) Add XY to both sides : AY = X + XY

iii) Factorise the right hand side : AY = X (1 + Y)

iv) Divide both sides by (1+Y) : AY/ (1+Y) = X

If you meant starting with Y = (X/A) - X then the procedure is similar

i) Factorise the right hand side Y = X (1/A-1) = X (1-A) / A

ii) Multiply both sides by A/(1-A) : X = YA/(1-A)

Answer 2

Multiply by A

AY =  X -AX

factor out X

AY = X(1-A)

divide by 1-A

AY/(1-A) = X

Answer 3

First add X to both sides, this will get rid of the -x on the one side, I'm hoping you are doing this with real numbers though :-D after that times A by both sides, getting rid of the A, then you will be left with X only on that one side!

Answer 4

As you have presented the question it can be read as :-

(i) y = (x / a) - x

OR

(ii) y = x / (a - x)

You have expressed the question in words but these don`t make sense either, unfortunately.

You have to make clear what you mean.

Will take a GUESS at (ii) :-

y = x / (a - x)

y (a - x) = x

ay - y x = x

ay = x + y x

ay = x (1 + y)

x = ay / (1 + y)