QuestionREVIEW: Solve the equation. Check your solutions. $$3-\frac{1}{t}-\frac{2}{t^{2}}=0$$
The solution set is \{ $\square$ \}. (Type an integer or a fraction. Use a comma to separate you

Studdy Solution
Check both solutions in the original equation to ensure they do not make any denominators zero and satisfy the equation:
For $t = 1$:
$$3 - \frac{1}{1} - \frac{2}{1^2} = 3 - 1 - 2 = 0$$
This is valid.
For $t = -\frac{2}{3}$:
$$3 - \frac{1}{-\frac{2}{3}} - \frac{2}{\left(-\frac{2}{3}\right)^2}$$
$$3 + \frac{3}{2} - \frac{2}{\frac{4}{9}}$$
$$3 + \frac{3}{2} - \frac{9}{2}$$
$$3 + \frac{3}{2} - \frac{9}{2} = 3 - 3 = 0$$
This is also valid.
The solution set is:
$$\boxed{1, -\frac{2}{3}}$$