SOLUTION: how to solve= 1/cube root 4+ cube root 2 +1 i know the ans is cube root 2 -1 but i dont know how to solve it

Question 957853: how to solve= 1/cube root 4+ cube root 2 +1

i know the ans is cube root 2 -1 but i dont know how to solve it

Found 2 solutions by Alan3354, jsmallt9:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
What is the denominator?
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Parentheses are free.
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
First of all, please put multiple-term numerators and denominators in parentheses. What you posted meant:

But I'm quite sure you meant:

which should be posted as:
1/(cube root 4+ cube root 2 +1)
Tutors are more likely to respond if problems are posted clearly.

Clearing cube roots from a multiple-term denominator involves use of one or both of the following patterns:
A relatively fast way to simplify this requires that we recognizing that . Substituting this into our expression we get:

Now we need to recognize that this denominator matches the pattern of the second factor of with an "a" of and a "b" of 1. The pattern shows us that if we multiply that factor by (a-b) then we get . With all terms being perfect cubes, this will eliminate the cube roots.

So we multiply the numerator and denominator by (a-b) with an "a" of and a "b" of 1:

In the denominator, the pattern tells us what we get. In the numerator we just use the Distributive Property:

Simplifying...

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