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Prove It You should be able to see straight away that $\displaystyle t \neq 1$ because it would create a $\displaystyle 0$ denominator.
$\displaystyle \frac{3t - 5}{t - 1} = 2 + \frac{2t}{1 - t}$
$\displaystyle \frac{3t - 5}{t - 1} = 2 - \frac{2t}{t - 1}$
$\displaystyle \frac{3t - 5}{t - 1} + \frac{2t}{t - 1} = 2$
$\displaystyle \frac{5t - 5}{t - 1} = 2$
$\displaystyle 5t - 5 = 2(t - 1)$
Okay, that's what was confusing me.. Thanks!
$\displaystyle 5t - 5 = 2t - 2$
$\displaystyle 3t = 3$
$\displaystyle t = 1$.
So what this means is that this function will be almost identical to a different function - the only difference being that there is a point of discontinuity at $\displaystyle t = 1$. Because of this point of discontinuity, this equation does not have a solution.