could you explain WHY an answer is what an answer is please?
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?
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.
j
To understand why the answer is -square root of 15 - 4, let's go through the steps again and pay close attention to the sign changes:
1. Starting with the rational expression: 1/square root of 15 - 4
We want to rationalize the denominator, so we multiply both the numerator and denominator by the conjugate: square root of 15 + 4.
2. Multiplying the numerator: 1 * (square root of 15 + 4) = square root of 15 + 4
3. Multiplying the denominator: (square root of 15 - 4) * (square root of 15 + 4) = (square root of 15)^2 - 4^2
The denominator simplifies to 15 - 16 = -1.
4. Now, the expression becomes: (square root of 15 + 4) / -1
Dividing by -1 changes the sign, so the expression becomes: -(square root of 15 + 4)
Hence, the answer is -square root of 15 - 4.
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"