Simplify the rational expression state any restrictions on the variable t² + t - 6/t² - 9

Solution:

Let f(t) = t² + t - 6/t² - 9 --- (1)

Now let us factorise the numerator

t² + t - 6 = t² + 3t - 2t -6

= t(t + 3) -2(t + 3)

= t(t + 3) - 2(t + 3)

= (t + 3)(t - 2) --- (2)

The denominator is t² - 9 is of the form a² - b² = (a - b)(a + b)

t² - 9 = t - 3

= (t + 3)(t - 3) --- (3)

Substituting (2) and (3) back in (1) we have

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

= (t - 2)/(t - 3), t ≠ 3

Simplify the rational expression state any restrictions on the variable t² + t - 6/t² - 9

Summary:

Simplifying the rational expression t² + t - 6/t² - 9 we obtain (t - 2)/(t - 3), t ≠ 3