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