# How do you solve 1/x + 1 = x/2?

Oct 29, 2015

We need to take all the variables ,i.e,x to one side and constants to one side.

#### Explanation:

1)given.1/x+1=x/2
2)bringing variables to one side and constants to one side,1=x/2-1/x
3)on calculating,taking2x as LCM in denominator we get 1=(${x}^{2}$-2)/2x
4)on cross multiplying ,we get 2x=(${x}^{2}$-2)
5)we get a quadratic eqn,so for solving this bringing 2x to the right side we get,${x}^{2}$-2-2x=0
6)for solving the value of x in such equations we apply this formula:-
x=
-b+-sqrt${b}^{2}$-4ac/2a

7) on further solving here values for a,b,c (coefficients) are 1,-2 and -2 respectively.
Sox=2+-$\sqrt{12}$/2....answer
,......................
I hope this helps.