Question

What is the excluded value of (y² + 1/y² - y - 6)?

a) (y = 0)
b) (y = 2)
c) (y = -2)
d) (y = 3)

Answer 1

The excluded value for the expression (y² + 1)/(y² - y - 6) is y = 3, because it is the value that would make the denominator zero, thus making the expression undefined. The correct multiple-choice option is d) (y = 3).

Step-by-step explanation:

The question asks to find the excluded value of the expression (y² + 1)/(y² - y - 6). The excluded values are vlues of y which would make the denominator equal to zero, as division by zero is undefined in mathematics. To find the excluded values, we set the denominator equal to zero and solve for y:

y² - y - 6 = 0

Factoring the quadratic equation we get:

(y - 3)(y + 2) = 0

This gives us two values for y:

• y = 3
• y = -2

Therefore, the excluded values are y = 3 and y = -2. However, looking at the multiple-choice options provided, the correct answer is d) (y = 3), because this is the option included in the choices given.