Question 178262
{{{sqrt(w)/(sqrt(w)+1)+sqrt(w)/(sqrt(w)-1)}}} Start with the given expression.



Take note that the LCD is {{{(sqrt(w)+1)(sqrt(w)-1)}}}



{{{(sqrt(w)/(sqrt(w)+1))((sqrt(w)-1)/(sqrt(w)-1))+sqrt(w)/(sqrt(w)-1)}}} Multiply the first fraction by {{{(sqrt(w)-1)/(sqrt(w)-1)}}} to get the denominator equal to the LCD



{{{(sqrt(w)*(sqrt(w)-1))/((sqrt(w)+1)(sqrt(w)-1))+sqrt(w)/(sqrt(w)-1)}}} Combine and multiply the fractions




{{{(sqrt(w)*(sqrt(w)-1))/((sqrt(w)+1)(sqrt(w)-1))+(sqrt(w)/(sqrt(w)-1))((sqrt(w)+1)/(sqrt(w)+1))}}} Multiply the second fraction by {{{(sqrt(w)+1)/(sqrt(w)+1)}}} to get the denominator equal to the LCD



{{{(sqrt(w)*(sqrt(w)-1))/((sqrt(w)+1)(sqrt(w)-1))+(sqrt(w)*(sqrt(w)+1))/((sqrt(w)-1)(sqrt(w)+1))}}} Combine and multiply the fractions




{{{(sqrt(w)*sqrt(w)+sqrt(w)(-1))/((sqrt(w)+1)(sqrt(w)-1))+(sqrt(w)*sqrt(w)+sqrt(w)(1))/((sqrt(w)+1)(sqrt(w)-1))}}} Distribute



{{{((sqrt(w))^2-sqrt(w))/((sqrt(w)+1)(sqrt(w)-1))+((sqrt(w))^2+sqrt(w))/((sqrt(w)+1)(sqrt(w)-1))}}} Multiply



{{{(w-sqrt(w))/((sqrt(w)+1)(sqrt(w)-1))+(w+sqrt(w))/((sqrt(w)+1)(sqrt(w)-1))}}} Square {{{sqrt(w)}}} to get "w"



{{{(w-sqrt(w)+w+sqrt(w))/((sqrt(w)+1)(sqrt(w)-1))}}} Combine the fractions (this is possible since the denominators are equal)



{{{(2w)/((sqrt(w)+1)(sqrt(w)-1))}}} Combine like terms.



{{{(2w)/((sqrt(w))^2-1^2)}}} FOIL the denominator (use the difference of squares formula)



{{{(2w)/(w-1)}}} Square {{{sqrt(w)}}} to get "w". Square 1 to get 1




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Answer:



So {{{sqrt(w)/(sqrt(w)+1)+sqrt(w)/(sqrt(w)-1)=(2w)/(w-1)}}} where {{{w>=0}}}