Question

Arrange the expressions in the correct sequence to rationalize the denominator of the expression:

-2 / (√(5) + y - 2)

Options:
A) -2(√(5) + y - 2) / (1 + y - 2 - y - 2)
B) -2(√(5) + y - 2 + y + 2) / (√(5) + y - 2 + y + 2)
C) -2(√(5) + y - 2 - √(5) + y + 2) / (√(5) + y - 2 - √(5) + y + 2)
D) -4(√(5) + y - 2 + √(5) + y + 2) / (-2√(5) + y - 2 + √(5) + y + 2)

Answer 1

To rationalize the denominator of the provided expression, multiply the numerator and the denominator by the conjugate of the denominator. The correct option for this process is C), which results in canceling the radicals and rationalizing the denominator.

Step-by-step explanation:

To rationalize the denominator of the expression -2 / (√(5) + y - 2), we need to multiply both the numerator and the denominator by the conjugate of the denominator. The conjugate of √(5) + y - 2 is √(5) - (y - 2), which is √(5) - y + 2.

The correct sequence of operations is to take Option C) -2(√(5) + y - 2 - √(5) + y + 2) / (√(5) + y - 2 - √(5) + y + 2) This will result in a rationalized denominator, as the radicals will cancel out in the denominator and leave a sum of rational terms.