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I am scratching my head to figure out a way to separate variables of the following equation:

$$(t+3)(t-2)dx = (t+tx^2)dt$$

Doesn't matter how many times I divide and multiply, I always get $x$ and $t$ on one side. Is there a trick applicable here?!

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$(t+tx^2) = t(1+x^2)$ – Antonio Vargas May 3 '12 at 23:38
up vote 3 down vote accepted

$$ (t+3)(t-2) dx = (t+tx^2)dt \Rightarrow (t+3)(t-2)dx=t(1+x^2) dt \Rightarrow \frac{dx}{1+x^2}=\frac{t}{(t+3)(t-2)} dt $$ I assume you can take it from here.

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