Question 1004483
.
solve
Sqrt(x/1-x)+Sqrt(1-x/x)=13/6 
where (x is not equal to 0,1)
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Introduce new variable  y = {{{sqrt(x/(1-x))}}}.
Notice that  {{{1/y}}} = {{{sqrt((1-x)/x)}}}.


Then your equation takes the form


{{{y}}} + {{{1/y}}} = {{{13/6}}}.


To solve it,  multiply both sides by 6y.  You will have


{{{6y^2}}} + {{{6}}} = {{{13y}}}.


Simplify:


{{{6y^2}}} - {{{13y}}} + {{{6}}} = {{{0}}}.


Apply quadratic formula.  You will get the roots  {{{y[1]}}} = {{{3/2}}}  and  {{{y[2]}}} = {{{2/3}}}.


Now you need to solve two equations to determine x.


First equation is  {{{sqrt(x/(1-x))}}} = {{{3/2}}}.
To solve it,  square first both sides.  Then . . .  (. . . as you are 9th grade,  you should know what do next . . . ).


The second equation is  {{{sqrt(x/(1-x))}}} = {{{2/3}}}.


Please complete the solution yourself. 


Good luck!