Question
(2sqrt(5))/(3 - sqrt(5))
Answers
GPT 3.5
To simplify the given expression, we need to rationalize the denominator by multiplying both the numerator and denominator by the conjugate of the denominator.
Given expression: (2√5)/(3 - √5)
Multiply both numerator and denominator by the conjugate of the denominator, which is (3 + √5):
[(2√5)(3 + √5)] / [(3 - √5)(3 + √5)]
Expanding the numerator and denominator:
= (6√5 + 2*5) / (3 * 3 - 3√5 + 3√5 - 5)
= (6√5 + 10) / (9 - 5)
= (6√5 + 10) / 4
The simplified expression is (3√5 + 5)/2.
Given expression: (2√5)/(3 - √5)
Multiply both numerator and denominator by the conjugate of the denominator, which is (3 + √5):
[(2√5)(3 + √5)] / [(3 - √5)(3 + √5)]
Expanding the numerator and denominator:
= (6√5 + 2*5) / (3 * 3 - 3√5 + 3√5 - 5)
= (6√5 + 10) / (9 - 5)
= (6√5 + 10) / 4
The simplified expression is (3√5 + 5)/2.