Simplification....

[johnkim4]

Manhattan GMAT Flash Cards: EIV's #30

Simplify: 3 / (2 + SQR3)

After multiplying the numerator and the denominator by the conjugate, I'm not seeing how the denominator reduces to 1.

[jnelson0612]

Manhattan GMAT Flash Cards: EIV's #30

Simplify: 3 / (2 + SQR3)

After multiplying the numerator and the denominator by the conjugate, I'm not seeing how the denominator reduces to 1.

I'm glad you know to multiply the numerator and denominator by the conjugate. That's great.

Okay, let's multiply the denominator and see what we get:
(2 + sqrt3)(2 - sqrt3)
FOIL gives us:
First: 2*2 = 4
Outside: 2 * - sqrt3 = -2sqrt3
Inside: sqrt3 * 2 = 2sqrt3
Last: sqrt3 * -sqrt3 = -3

Now, add them together: 4 + (-2sqrt3) + 2sqrt3 + (-3)

The two middle terms cancel out, and we are left with 4 - 3 = 1.