What are the domain of the Group A equations?

x² - 1 = 0

Domain: (-∞, ∞)

(x + 7) = x² + 49

Domain: (-∞, ∞)

(x² - 4)/(x - 2) = 2x - 1

Domain: (-∞, ∞)

What are the domain of the Group B equations?

x² - 1 = (x - 1)(x + 1)

Domain: (-∞, ∞)

(x + 7)² = x² + 14x + 49

Domain: (-∞, ∞)

(x² - 4)/(x - 2) = x + 2

Domain: (-∞, ∞)

Which group of equations is true for only one real number?

Group A is true for only one real number

x² - 1 = 0

(x + 1)(x - 1)

x = -1 ; x = 1

(x + 7) = x² + 49

x + 7 = x² + 49

x² - x + 42 = 0

(x² - 4)/(x - 2) = 2x - 1

(x + 2)(x - 2)/(x - 2) = 2x - 1

x + 2 = 2x - 1

x - 2x + 2 + 1 = 0

-x + 3 = 0

-x = -3

x = 3

Which group of equations is true for all real numbers?

Group B is true for all real numbers

x² - 1 = (x - 1)(x + 1)

x² - 1 = x² - 1

0 = 0 ; true

(x + 7)² = x² + 14x + 49

(x² + 14x + 49 = x² + 14x + 49

0 = 0 ; true

(x² - 4)/(x - 2) = x + 2

(x² - 4) = (x - 2)(x + 2)

x² - 4 = x² - 4 ;

0 = 0 ; true

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