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Really basic question, I just can't get it.

I have $yt - y = 2t$. I want to solve it in terms of $t$ rather than $y$. The answer is $t = \frac{y}{y-2}$.

How do I isolate the $t$ on one side and the $y$'s on the other? I considered factoring the left-hand side into $y(t - 1)$, but i couldn't get anywhere with it. I suppose I could subtract $yt$ from both sides, then try again. Any help?

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You want to "isolate" $t$, so you want to bring all the $t$ stuff to one side. – André Nicolas Feb 4 '13 at 5:48
up vote 3 down vote accepted

We proceed as follows: $$\begin{align*} yt-y&=2t\\ yt&=y+2t\\ yt-2t&=y\\ t(y-2)&=y\\ t&=\tfrac{y}{y-2} \end{align*}$$ We should be careful to note that this answer is correct only when $y\neq 2$; otherwise we would be dividing by zero.

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Thanks very much - I was trying to factor then add inverses, I had the process backwards. Cheers! – Peter Feb 4 '13 at 5:57
Glad I could help! – Zev Chonoles Feb 4 '13 at 6:04

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