Solve Q= (N-S)/ N for N

So when I multiply both sides by N
I get Q(N)= N-S
I know I am doing something wrong, the answer is in the book which is
N=S/(1-Q)but I don't understand were the 1 comes from. Could you write it out step by step, so I can see what I don't yet understand?

Here's one way to solve for N.

Q = (N - S)/N

Factor out N in the numerator:

Q = N(1 - S/N)/N

Cancel out N in both numerator and denominator to end up with this:

Q = 1 - S/N

Subtract 1 from both sides:

Q - 1 = - S/N

Multiply both sides by N:

N(Q - 1) = - S

Divide both sides by (Q - 1):

N = - S/(Q - 1)

Factor out -1 to end up with this:

N = S / (1 - Q)

I hope this will help.

thanks, I would have never gotten that far. I didn't know that the N could be factored out like that- to get 1, so with this knowledge I try other problems and see if it works out for me.

You're welcome! I'm glad I could help. Factoring out N in the numerator is a helpful technique to simplify expressions. It allows you to cancel out N in both numerator and denominator, which often leads to a simpler form of the equation.

Feel free to try other problems and see if this technique works for you. Remember to always be careful with canceling out variables or terms, as there might be restrictions or special cases to consider. If you have any more questions, feel free to ask!