Question

Consider the following rational expression. x² + 5x - 24 / r² - 10x + 21. Determine what value(s), if any, of the variable must be excluded.

a) 0
b) 3
c) -7
d) 5

Answer 1

b) 3. c) -7.To find the values of the variable that must be excluded in the given rational expression, we set the denominator equal to zero and solve. The values 3 and -7 must be excluded.

Step-by-step explanation:

To determine the values of the variable that must be excluded in the given rational expression, we need to identify any values that would make the denominator equal to zero. In this case, we have the expression:

(x² + 5x - 24) / (r² - 10x + 21)

For the denominator to be equal to zero, we set it equal to zero and solve:

r² - 10x + 21 = 0

By factoring or using the quadratic formula, we find that the values of x that would make the denominator equal to zero are:

x = 3, -7

Therefore, the values 3 and -7 must be excluded from the domain of the variable.