Answer:
1).
2).
Step-by-step explanation:
In this question we have to write the fractions in the factored form.
Rational expressions are and
.
1).
Factored form of the denominator (x² - x - 12) = x² - 4x + 3x - 12
= x(x - 4) + 3(x - 4)
= (x + 3)(x - 4)
Therefore.
2).
Factored form of the denominator (x² - 16) = (x - 4)(x + 4)
[Since (a²- b²) = (a - b)(a + b)]
Therefore,
If p and q are both true, then
is an implication of the form
which is true, because every implication starting with false is true, i.e.
So, we're looking for an expression evaluating to true. Let's see what we have:
A) is an AND proposition. Logical AND is true only if both parts are true. So, you have
So it's not the right option.
B) is an OR proposition. Logical OR is true whenever one of the two parts is true. So, you have
So it's not the right option.
C) is again an AND proposition. You have
So this is not the right option.
D) Finally, the last one is again an implication, and again it starts with false:
So this is true, and thus is the correct option.