Find all numbers for which the rational expression is undefined.
p^3 - 4p/P^2 - 4
Did you leave out some parentheses? What is the denominator? What is the numerator?
The expression, whatever it is, is undetermined when a denominator is zero
To find the values for which a rational expression is undefined, we need to identify the values that would make the denominator equal to zero.
In this case, the given rational expression is (p^3 - 4p) / (P^2 - 4).
To identify the values of p that would make the denominator zero, we set the denominator equal to zero and solve for p:
P^2 - 4 = 0
We can factor the equation as a difference of squares:
(P + 2)(P - 2) = 0
Now we can determine the values of p that make the quadratic equation equal to zero. Since the product of two factors is zero, either (P + 2) = 0 or (P - 2) = 0:
For (P + 2) = 0, solving for P:
P = -2
For (P - 2) = 0, solving for P:
P = 2
Therefore, the rational expression is undefined for p = -2 and p = 2, as these values would make the denominator zero, which is not allowed in rational expressions.