(t^(2)+t-6)/(t^(2)-9) Simplify the rational expression. State any restrictions on the variable
To simplify the rational expression (t^(2)+t-6)/(t^(2)-9), we first factor the numerator and 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)
Notice that (t + 3) appears in both the numerator and denominator. We can cancel it out to simplify the expression:
(t - 2) / (t - 3)
Therefore, the simplified expression is (t - 2) / (t - 3).
Restrictions on the variable:
The original expression is not defined when the denominator is equal to zero, so we must find the values of t that make the denominator zero:
t^(2) - 9 = 0
(t + 3)(t - 3) = 0
t = -3 or t = 3
Therefore, the restrictions on the variable are t ≠ 3 and t ≠ -3.