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Grammar in mathematics is important so that the question cannot be misunderstood.
The question is asking for the solution to 1/(x + 8) + 6/(x - 8).
Where fractions are being added or subtracted then the denominators need converting to a common denominator. With numbers this new denominator would be the Lowest Common Multiple. With algebraic terms then simply take the product.
The common multiple of (x + 8) and (x - 8) is (x + 8)(x - 8) = x2 - 82
1/(x + 8) = 1 x (x - 8)/x2 - 82 = x - 8/x2 - 82
6/(x - 8) = 6 x (x + 8)/x2 - 82 = 6x + 48/x2 - 82
1/(x + 8) + 6/(x - 8) = x - 8/x2 - 82 + 6x + 48/x2 - 82 = 7x + 40/x2 - 82
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