We have to determine if 2x/(x+5) - x/(x-5) = 50/(25-x^2) has any solutions.

2x/(x+5) - x/(x-5) = 50/(25-x^2)

=> [2x(x - 5) - x(x + 5)] / (x^2 - 25) = 50 / (25-x^2)

=> 2x^2 - 10x - x^2 - 5x + 50 = 0

=> x^2 - 15x...

## Unlock

This Answer NowStart your **48-hour free trial** to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime.

Already a member? Log in here.

We have to determine if 2x/(x+5) - x/(x-5) = 50/(25-x^2) has any solutions.

2x/(x+5) - x/(x-5) = 50/(25-x^2)

=> [2x(x - 5) - x(x + 5)] / (x^2 - 25) = 50 / (25-x^2)

=> 2x^2 - 10x - x^2 - 5x + 50 = 0

=> x^2 - 15x + 50 = 0

=> x^2 - 10x - 5x + 50 = 0

=> x(x - 10) - 5(x - 10) = 0

=> (x - 5)(x - 10) = 0

x = 5 and x = 10

But x = 5 makes x/(x-5) indeterminate

**So the required solution of the equation is x = 10**