Simplify the rational expression. State any restriction on the variable.
t^2+t-30 / t^2-25
First factor the numerator and denominator:
(t^2 + t - 30) / (t^2 - 25)
Numerator factors to (t + 6)(t - 5) and the denominator factors to (t + 5)(t - 5):
= (t + 6)(t - 5) / (t + 5)(t - 5)
Now, we can cancel out the common factor of (t - 5) from both the numerator and denominator:
= (t + 6) / (t + 5)
Therefore, the simplified rational expression is (t + 6) / (t + 5) with a restriction on the variable t that t cannot be equal to -5 (to avoid division by zero).