Solve the equation. `5((x+2)/(x-2))^2 - 2((x+2)/(x-2)) - 3 = 0` Hint: Use `u = (x+2)/(x-2)` and solve for `x` .  Enter the solutions separated by commas. 

Expert Answers
tiburtius eNotes educator| Certified Educator


Substitution `u=(x+2)/(x-2)`


Now you use the formula for solution of quadratic equation

`x_(1,2)=(-b pm sqrt(b^2-4ac))/(2a)` where `a,b` and `c` are coefficients of the equation. 


`u_1=-5/2,` `u_2=3/2`

Now we put `u_1` back in our substitution


Multiply whole equation by `4(x-2)`





Now we put `u_2` back into our substitution. ` `


Multiply whole equation by `2(x-2)`




Hence your solutions are `x_1=2/9`  , `x_2=10.`  

aruv | Student



`t=(x+2)/(x-2)`  and `t!=2`  otherwise  t is not defined.





`=> t=-3/5 or t=1`






`=> (x+2)/(x-2)!=1`

`i.e. t=1`  not possible.









Thus solution of above quadratic equation is x=-1/2 .