Simplify fraction

[songoku]

1. The problem statement, all variables and given/known data
Simplify

\frac{2}{49^{1/3}+7^{1/3}+1}


2. Relevant equations



3. The attempt at a solution
I can simplify
\frac{2}{49^{1/3}+7^{1/3}}

but I don't have idea how to do this one..

EDIT: I have found it. No need to reply this. Thanks :)

[SammyS]

1. The problem statement, all variables and given/known data
Simplify

\frac{2}{49^{1/3}+7^{1/3}+1}
...

3. The attempt at a solution
I can simplify
\frac{2}{49^{1/3}+7^{1/3}}

but I don't have idea how to do this one..

EDIT: I have found it. No need to reply this. Thanks :)
I see that you have found it, but for others looking later:

Multiply the numerator & denominator by \displaystyle (7^{1/3}-1)

[songoku]

I see that you have found it, but for others looking later:

Multiply the numerator & denominator by \displaystyle (7^{1/3}-1)

I did it another way but let discuss your way. I drop the numerator because we only concern about the denominator.

After multiplying it with 71/3 - 1, I get:
491/3 . 71/3 - 491/3 + 72/3 - 1

I think I have to multiply the denominator with another term but I can't find it..

[SammyS]

49=72 so the denominator becomes 6 .

491/3 ∙ 71/3 - 491/3 + 72/3 - 1

= 72/3 ∙ 71/3 - 72/3 + 72/3 - 1

= 7 - 1

[songoku]

49=72 so the denominator becomes 6 .

491/3 ∙ 71/3 - 491/3 + 72/3 - 1

= 72/3 ∙ 71/3 - 72/3 + 72/3 - 1

= 7 - 1

It really didn't cross my mind; multiplying with (71/3 - 1) will directly give the answer. Your method is much simpler than mine. I should have noticed the pattern a^2 + a + 1 in the denominator, which can be simplified by multiplying it with (a - 1)

Thanks :)