Question 132974
All you need to do is substitute the given value for x into the expression and then do the arithmetic.


If you meant {{{x=sqrt(6/7)}}}, then evaluate {{{(x+1/x)^2}}}, that means you need to evaluate:


{{{(sqrt(6/7)+1/sqrt(6/7))^2}}}


Apply FOIL:
{{{(sqrt(6/7))^2+(sqrt(6/7))(1/(sqrt(6/7)))+(sqrt(6/7))(1/(sqrt(6/7)))+(1/sqrt(6/7))^2}}}


{{{6/7+1+1+(1/(6/7))=6/7+2+7/6}}}


LCD is 42, so:
{{{36/42+84/42+49/42=169/42}}}


Since 169 (13 * 13) and 42 (2 * 3 * 7) have no common factors, this is reduced to lowest terms.


On the other hand, if you meant: {{{x=sqrt(6)/7}}}, then evaluate {{{(x+1/x)^2}}}, that means you need to evaluate:


{{{(sqrt(6)/7+1/(sqrt(6)/7))^2}}}


Apply FOIL:
{{{(sqrt(6)/7)^2+(sqrt(6)/7)(1/(sqrt(6)/7))+(sqrt(6)/7)(1/(sqrt(6)/7))+(1/(sqrt(6)/7))^2}}}


{{{6/49+1+1+(1/(6/49))=6/49+2+49/6}}}


LCD is 294, so:
{{{36/294+588/294+2401/294=3025/294}}}


Since 3025 (5 * 5 * 11 * 11) and 294 (2 * 3 * 7 * 7) have no common factors, this is reduced to lowest terms.