# Thread: Changing the subject of a formula

1. ## Changing the subject of a formula

Hello

I'm trying to learn algebra and am working through a book doing all the practice exercises. There is one question in particular under the subject of changing the subject of a formula that I don't know how the answer was derived.

The question is:

Make y the subject of

I can't figure out how they've come to that answer and there is no explanation in the book. Can anyone help please?

Thanks

2. Originally Posted by Natter
Hello

I'm trying to learn algebra and am working through a book doing all the practice exercises. There is one question in particular under the subject of changing the subject of a formula that I don't know how the answer was derived.

The question is:

Make y the subject of

I can't figure out how they've come to that answer and there is no explanation in the book. Can anyone help please?

Thanks
First step is to multiply both sides by xy, the denominator of the left, to get:

$\displaystyle y + x = xy(p + q)^2$

Now how do you think you should proceed? to solve for y, you need to get y by itself on one side. you can start by getting all terms with y's in them on one side.

3. Make your life easier: let k = (p+q)^2; then you have:
(x + y) / (xy) = k
x + y = kxy
kxy - y = x : get it?

4. Thanks everyone. No Wilmer, I don't understand that.

Skeeter, you also sent me a reply and I have it in my email but can't see it in the actual thread anymore. I understand your rational up to the step after you subtract y from both sides. So to confirm I understand Step 1 is to multiply by xy and Step 2 is to subtract y. But then I completely don't understand the next step where 1 is subtracted. Where does the 1 come from?? Thanks all! Sorry, I probably sound really thick!!

5. I've worked it out! You then factorise it which is how the 1 is obtained, and then divide by the new factorise equation. Thanks for all help!!

6. Originally Posted by Natter
I've worked it out! You then factorise it which is how the 1 is obtained, and then divide by the new factorise equation. Thanks for all help!!
Correct!

Make your life easier: let k = (p+q)^2; then you have:
(x + y) / (xy) = k
x + y = kxy
kxy - y = x : get it?

Factorize:
y(kx - 1) = x
Divide by kx-1:
y = x / (kx - 1)
Substitute back in:
y = x / [x(p + q)^2 - 1]