Simplify each rational expression. State all non-permissive values (restrictions).

Question

𝑚^2−𝑚−12 / 𝑚+2 ÷ 3𝑚^2−3𝑚−36 / 𝑚^2−9

Answer 1

To simplify the rational expression, we need to factor the numerators and denominators.

𝑚^2 − 𝑚 − 12 / 𝑚 + 2 can be factored as (m - 4)(m + 3).
3𝑚^2 − 3𝑚 − 36 can be factored as 3(m - 4)(m + 3).
𝑚^2 − 9 can be factored as (m - 3)(m + 3).

Now we can rewrite the rational expression:

((m - 4)(m + 3) / (m + 2)) / ((3(m - 4)(m + 3)) / ((m - 3)(m + 3)))

When dividing rational expressions, we can multiply the first expression by the reciprocal of the second expression:

((m - 4)(m + 3) / (m + 2)) * (((m - 3)(m + 3)) / (3(m - 4)(m + 3)))

Now simplify by canceling out common factors:

((m - 4) / 1) * (1 / (3(m - 4)))

The (m + 3) and (m - 3) factors canceled out.

Simplifying further:

(m - 4) / (3(m - 4))

The non-permissive value is m = 4, as it would cause division by zero in the original expression.