Question

Rationalize the denominator.2/(3+ (2√3)

Answer 1

To rationalize the denominator, multiply both the numerator and the denominator by the conjugate of the denominator. Simplify the resulting expression to obtain the rationalized form of the denominator.

Step-by-step explanation:

To rationalize the denominator, we need to eliminate the square root from the denominator. We can do this by multiplying both the numerator and denominator by the conjugate of the denominator. The conjugate of 3 + (2√3) is 3 - (2√3). So, multiplying the expression by the conjugate resolves the square root in the denominator.

Using the distributive property, we get:

(2/(3 + (2√3))) * ((3 - (2√3))/(3 - (2√3)))

Simplifying the numerator and denominator, we have:

(4 - 2√3)/(9 - 12)

Which simplifies further to:

(4 - 2√3)/(-3)

So, the rationalized form of the denominator is -(4 - 2√3)/3.