How do you rationalize the denominator and simplify $1/(1+root3x+root3(x^2)$ #?

Question

1385 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-09-24T19:57:55

Refer to explanation

Set $t=root(3) x$ hence we have that

$1/(1+t+t^2)$

We know that $t^3-1=(t-1)*(1+t+t^2)=>1+t+t^2=(t^3-1)/(t-1)$

hence

$1/(1+t+t^2)=1/((t^3-1)/(t-1))=(t-1)/(t^3-1)$

because $t=root(3) x$

we replace it and get

$(root(3) x -1)/(((root(3) x)^3)-1)=(root(3) x-1)/(x-1)$

How do you rationalize the denominator and simplify 1/(1+root3x+root3(x^2)1/(1+root3x+root3(x^2)#?