Question 88323
In general, when you have an equation with denominators, get rid of them.
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Multiply thru by (x-5)(x+5) to get:

9/(x-5) - 1 = 8/(x+5)

9(x+5) - (x-5)(x+5) = 8(x-5)

9x+45 - (...)(...) = 8x-40
x + 85 -[x^2-25] = 0
-x^2+x+110 = 0
x^2 -x -110 = 0
(x-11)(x+10) = 0
x = 11 or x = -10

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Cheers,
Stan H.