`a+1=2sqrt(a)x` then `(sqrt(x^2-1))/(x-sqrt(x^2-1))=`

If x=(1)/(2)(sqrt(a)+(1)/(sqrt(a))) , then show that (sqrt(x^(2)-1))/(x-sqrt(x^(2)-1))=(a-1)/(2) .

If (x+sqrt(x^2-1))/(x-sqrt(x^2-1))+(x-sqrt(x^2-1))/(x+sqrt(x^2-1))= 14 ,then find the value of x.

Simplify : (a) sqrt(y+sqrt(2xy-x^(2))) + sqrt(y-sqrt(2xy-x^(2))) (b) (x+sqrt(x^2-1))/(x-sqrt(x^(2)-1)) -(x-sqrt(x^(2)-1))/(x+sqrt(x^(2)-1))

If x=(1)/(2)(sqrt(7)+(1)/(sqrt(7))) ,then , log_(27)((sqrt(x^(2)-1))/(x-sqrt(x^(2)-1))) is equal to

lim_(x rarr1)(sqrt(x^(2)-1)+sqrt(x-1))/(sqrt(x^(2)-1))

Simplify (x+sqrt(x^(2)-1))/(x-sqrt(x^(2)-1))+(x-sqrt(x^(2)-1))/(x+sqrt(x^(2)-1))

Evaluate lim_(x rarr 1) (sqrt(x^(2)-1)+sqrt(x-1))/(sqrt(x^(2)-1))

sqrt(x+2sqrt(x-1))+sqrt(x-2sqrt(x-1))>(3)/(2)

Differentiate the following function (sqrt(x^2+1)+sqrt(x^2-1))/(sqrt(x^2+1)-sqrt(x^2-1)

If x+sqrt(x^(2)-1)+(1)/(x+sqrt(x^(2)+1))=20 then x^(2)+sqrt(x^(4)-1)+(1)/(x^(2)+sqrt(x^(4)-1))=