SOLUTION: Rationalize 2A/B1/3

Question 514219: Rationalize 2A/B1/3
Answer by xdragonfight(116) (Show Source): You can put this solution on YOUR website!
a) (1/√2)/(1 − (1/√2)) * (1 + (1/√2))/(1 + (1/√2))
= [(1/√2) * (1 + (1/√2))] / (1 - 1/2)
= [(1/√2) + 1/2] / (1/2)
= 1 + (2/√2)
= (√2 + 2)/√2 * √2/√2
= 1 + √2
Edit: a) can be simplified first:
a) (1/√2)/(1 − (1/√2))
= 1/(√2 - 1) * (√2 + 1)/(√2 + 1)
= (√2 +1)/(2 - 1)
= 1 + √2
Also b) can be simplified:
b) (1 + (1/√2))/(1 − (1/√2))
= (√2 + 1)/ √2 / (√2 - 1) / √2
= (√2 + 1) / (√2 - 1) * (√2 + 1) / (√2 + 1)
= (√2 + 1)^2 / (2 - 1)
= 3 + 2√2
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