(x+1)/(x-2)=3/(x-2)+5 - Wolfram|Alpha

Why on earth can't I just multiply by (t-2) and get the solution t=2 ?!

To make it absolutely clear that I should be able to just multiply by (t-2), I can rewrite this equation as:

$\displaystyle \frac{t+1}{t-2}=\frac{5t-7}{t-2}$

I am VERY confused..

I do realize that t can't be 2 because of the denominator becoming 0, but why does it give me the algebraic solution t=2 and then it doesn't work?