Simplify the rational expression. State any restrictions on the variable.

Question

(t^2 + t - 6)/(t^2 - 9)

Answer 1

To simplify the rational expression (t^2 + t - 6)/(t^2 - 9), we first factor the numerator and the denominator:

Numerator: (t^2 + t - 6) = (t + 3)(t - 2)
Denominator: (t^2 - 9) = (t + 3)(t - 3)

Now, we can rewrite the expression as:

(t + 3)(t - 2) / (t + 3)(t - 3)

We can cancel out the common factor (t + 3) in the numerator and the denominator:

(t - 2) / (t - 3)

Therefore, the simplified rational expression is (t - 2) / (t - 3). The restriction on the variable t is t ≠ 3, since that would make the denominator equal to zero.