What is one over x plus eight plus six over x minus eight?

Answer 1

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