Simplify the rational expression. State any restrictions on the variable. t^2+t−6/ t^2−9

Answer 1

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

(t^2 + t - 6) = (t + 3)(t - 2)
(t^2 - 9) = (t + 3)(t - 3)

Now, divide out the common factor of (t + 3) from both the numerator and denominator:

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

Now cancel out the common factor of (t + 3) from the numerator and denominator:

(t - 2) / (t - 3)

Therefore, the simplified rational expression is (t - 2)/(t - 3) with a restriction that t cannot equal 3.