Which rational expression does not have any excluded values?

a. x+2/2x2

b. 2x+4/3x+3

c. 6x-5/x2-7

d. x+2/-x2-5

d. (x+2) / (-x²-5)

Step-by-step explanation

ƒ (x) = x + 2 / (2x²)

The function is undefined when x = 0.

b. ƒ (x) = (2x + 4) / (3x + 3)

The function is undefined when 3x + 3 = 0, i. e., when x = - 1.

c. ƒ (x) = (6x - 5) / (x² - 7)

The function is undefined when x² - 7 = 0, i. e., when x = √7.

d. ƒ (x) = (x+2) / (-x²-5) = - (x+2) / (x² + 5)

The function would be undefined if x² + 5 = 0, i. e., if x² = - 5. However, the square of a real number cannot be negative.

This function has no excluded values.