Final answer:
To prove that 2/((sqrt of 3)/2) equals (4 sqrt 3)/3, multiply the numerator and denominator by the reciprocal of the denominator, simplify, and then rationalize the denominator to arrive at the simplified form.
Step-by-step explanation:
To find how 2/((sqrt of 3)/2) equals (4 sqrt 3)/3, you multiply the numerator and denominator of the fraction by the reciprocal of the denominator. In this case, you would multiply by 2/(sqrt of 3) because the reciprocal of (sqrt of 3)/2 is 2/(sqrt of 3). By doing this, we eliminate the complex fraction.
Step 1: Multiply numerator and denominator by 2/(sqrt of 3):
2/((sqrt of 3)/2) * 2/(sqrt of 3).
Step 2: Simplify:
(2 * 2) / (sqrt of 3 * 2/2) = 4/(sqrt of 3).
Step 3: Rationalize the denominator by multiplying numerator and denominator by sqrt of 3:
4/(sqrt of 3) * (sqrt of 3)/(sqrt of 3) = (4 * sqrt of 3)/(3).
Through these steps, we see how 2 divided by the fraction ((sqrt of 3)/2) can indeed be expressed as (4 sqrt 3)/3.