could you explain WHY an answer is what an answer is please?

Question

I have rational expression: 1/square root of 15 - 4
Only the 15 is under the square root, the -4 is not

I multiplied by the conjugate, so I multiplied by square root of 15 + 4

in the numerator I got square root of 15 + 4

In the denominator I got 15 - 4 = 11

The answer, however, is -square root of 15 - 4

HOW please?

Answer 1

The answer is -square root of 15 - 4 because when you multiply a rational expression by its conjugate, the numerator and denominator will both be perfect squares. In this case, the numerator is the square of the square root of 15 + 4, and the denominator is the square of 11. Since the numerator and denominator are both perfect squares, the answer can be simplified to -square root of 15 - 4.

Answer 2

recall that (a-b)(a+b) = a^2 - b^2
So, you can use that to rationalize the denominator
1/(√15 - 4) * (√15 + 4)/(√15 + 4) = (√15 + 4)/(15-16) = -(√15 + 4)

not sure how you came up with "the denominator is the square of 11"

Answer 3

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