Simplify the rational expression. State any restrictions on the variable.
t squared plus 4 times t minus twelve over t squared minus four
We can factor the numerator and denominator to simplify the expression:
(t^2 + 4t - 12) / (t^2 - 4) = [(t + 6)(t - 2)] / [(t + 2)(t - 2)]
Simplifying further, we can cancel out the common factor of (t - 2) in both the numerator and denominator:
(t + 6) / (t + 2)
Therefore, the simplified rational expression is (t + 6) / (t + 2). The only restriction on the variable is that t cannot be equal to 2 or -2, as these values would make the denominator zero and result in an undefined expression.