Question

Rationalize the following: 1/(√-7 - √3)

A. (√7 + √3)/4

B. (√7 - √3)/4

C. 4/(√7 + √3)

D. 4/(√7 - √3)

Answer 1

To rationalize the expression 1/(√-7 - √3), multiply the numerator and denominator by the conjugate of the denominator (√-7 + √3) to eliminate the square root in the denominator.

Step-by-step explanation:

To rationalize the expression 1/(√-7 - √3), you can multiply the numerator and denominator by the conjugate of the denominator (√-7 + √3). This will eliminate the square root in the denominator. Here's the step-by-step process:

1. Multiply the numerator and denominator by (√-7 + √3): 1/(√-7 - √3) * (√-7 + √3)/(√-7 + √3)
2. Apply the distributive property to the numerator: (√-7 + √3)/(√-7 + √3)
3. Use the difference of squares formula to simplify the denominator: (√-7 + √3)(√-7 - √3) = -7 - √21 + √21 - 3 = -10
4. Cancel out like terms: -7 + √21 + √21 - 3 = -10

Therefore, the rationalized expression is (-7 + 2√21)/(-10). Therefore, the correct answer is B. (-7 + 2√21)/(-10).