Clearly in this question we need to see all the values in which denominator is not 0 and the value inside the root is not negative.
Hence, x^2 - 7x - 8 > 0
x^2 - 8x + x - 8 > 0
x ( x - 8 ) + 1 ( x - 8 ) > 0
( x + 1 ) ( x - 8 ) > 0
Hence, the required subset becomes.
( - infinite , -1 ) and ( 8 , infinity )
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