Simplify the rational expression. state any restrictions state any restriction on the variable.
t^2+t-6/ t^2-9
a) t-2/t-3, t doesn't equal 3, t doesn't equal -3
b) t+2/ t-3, t doesn't equal 3
c) t+2/t+3, t doesn't equal 3, t doesn't equal -3
d) t+2/ t-3, t doesn't equal 3, t doesn't equal -2
The correct answer is b) t+2/ t-3, t doesn't equal 3.
To simplify the expression (t^2+t-6)/(t^2-9), we first factor the numerator and denominator.
Numerator: t^2 + t - 6 factors into (t+3)(t-2)
Denominator: t^2 - 9 factors into (t+3)(t-3)
Now we can cancel out the common factor (t+3), which leaves us with (t-2)/(t-3).
The restriction on the variable is t doesn't equal 3 because it results in a zero denominator in the original expression.