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

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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...

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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

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