Verify if the equation has any solutions 2x/(x+5)-x/(x-5)=50/(25-x^2) .

First, we'll impose the constraints of existence of the
fractions. All denominators have to be different from zero, for the fractions to
exist.

x + 5 different from 0 => x different from
-5

x - 5 different from 0 => x different from
5

The solutions of the equation can have any real value,
except the values {-5 ; 5}.

We'll solve the
equation:

2x(x-5) - x(x+5) =
50

2x^2 - 10x - x^2 - 5x =
50

We'll combine like
terms:

x^2 - 15x - 50 =
0

We'll apply quadratic
formula:

x1 = [15+sqrt(225 -
200)]/2

x1 = (15 + 5)/2

x1 =
10

x2 = (15-5)/2

x2 =
5

Since x2 = 5 is an exceted value, we'll reject this
solution.

The equation will have only one
real solution: x = 10.