How do you solve #\frac { x + 1} { x } = \frac { x } { 2}#?

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Answer 1 · 2016-12-30T16:12:07

#(x - 1 + sqrt 3) (x - 1 - sqrt 3)#

At first do the cross multiplication. i.e. #2*(x+1) = x*x#

#rArr 2x + 2 = x^2#

#rArr x^2 - 2x - 2 = 0#

#rArr x^2 - 2x +1 - 3 = 0 #

#rArr ( x - 1 )^2 - (sqrt 3)^2#

#rArr [(x - 1) + sqrt 3] [(x - 1) - sqrt 3]#

#rArr (x - 1 + sqrt 3) (x - 1 - sqrt 3)#