Make x the subject of y = √2x+1/x-1

Question

Make x the subject of y = √2x+1/x-1

Answer 1

if you mean y = sqr(2x+1)/(x-1)

then

xy-y = sqr(2x+1)

square both sides

x^2y^2 - 2xy^2 + y^2 = 2x + 1

combine like terms, treating x as the variable, for like terms

x^2y^2 -2x -2xy^2 + y^2 = 1

x^2y^2 -(2+2y^2)x + y^2 - 1 = 0

use the quadratic formula

x = (2+2y^2)/(2y^2) + or - (1/2y^2)sqr((2+2y^2)^2 -4(y^2)(y^2-1)