(х+3/х-3) + (х-3/х+3)

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вопрос

To simplify the expression (x + 3/x - 3) + (x - 3/x + 3), we need to find a common denominator for the two fractions.

First, let's simplify the individual fractions:

(x + 3/x - 3) = (x^2 + 3) / (x - 3)
(x - 3/x + 3) = (x^2 - 3) / (x + 3)

Now, let's add the two fractions together:

((x^2 + 3) / (x - 3)) + ((x^2 - 3) / (x + 3))

To find a common denominator, we multiply the first fraction by (x + 3) / (x + 3) and the second fraction by (x - 3) / (x - 3):

((x^2 + 3)(x + 3) + (x^2 - 3)(x - 3)) / ((x - 3)(x + 3))

Expanding the numerators:

(x^3 + 3x + 3x + 9) + (x^3 - 3x - 3x + 9) / (x^2 - 9)

Combining like terms:

2x^3 + 2x + 2x + 18 / x^2 - 9

2x^3 + 4x + 18 / x^2 - 9

Therefore, the simplified form of the expression (x + 3/x - 3) + (x - 3/x + 3) is (2x^3 + 4x + 18) / (x^2 - 9).