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

1 Answer

Answer:

Refer to explanation

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)#