Question 186820
{{{(x^(1/2) -(1/4)x^(-1/2) ) ^2}}} Start with the given expression.



{{{(x^(1/2) -(1/4)/(x^(1/2)) ) ^2}}} Rewrite {{{x^(-1/2)}}} as {{{1/x^(1/2)}}}



{{{(sqrt(x) -(1/4)/(sqrt(x))) ) ^2}}} Convert to radical notation



{{{(sqrt(x) - 1/(4*sqrt(x)) ) ^2}}} Multiply and simplify



{{{(sqrt(x))(sqrt(x))+(sqrt(x))(-1/(4*sqrt(x)))+(-1/(4*sqrt(x)))(sqrt(x))+(-1/(4*sqrt(x)))(-1/(4*sqrt(x)))}}} FOIL




{{{(sqrt(x))^2+(sqrt(x))(-1/(4*sqrt(x)))+(-1/(4*sqrt(x)))(sqrt(x))+(-1/(4*sqrt(x)))^2}}} Multiply



{{{x+(sqrt(x))(-1/(4*sqrt(x)))+(-1/(4*sqrt(x)))(sqrt(x))+1/(16x)}}} Square the square roots to eliminate them



{{{x-1/4-1/4+1/(16x)}}} Multiply



{{{x-1/2+1/(16x)}}} Combine like terms.



So {{{(x^(1/2) -(1/4)x^(-1/2) )^2=x-1/2+1/(16x)}}}