9/(5-√7)+22/(7+√5)-1/(√7+√5)

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вопрос

To simplify this expression, we first need to rationalize the denominators of the fractions.

Rationalize the denominator of the first fraction: 5 - √7

Multiply both the numerator and denominator of the first fraction by the conjugate of the denominator:
9/(5-√7) * (5+√7)/(5+√7) = 9(5+√7)/(25 - 7) = 9(5+√7)/18 = (5+√7)/2

Rationalize the denominator of the second fraction: 7 + √5

Multiply both the numerator and denominator of the second fraction by the conjugate of the denominator:
22/(7+√5) * (7-√5)/(7-√5) = 22(7-√5)/(49 - 5) = 22(7-√5)/44 = (7-√5)/2

Rationalize the denominator of the third fraction: √7 + √5

Multiply both the numerator and denominator of the third fraction by the conjugate of the denominator:
1/(√7+√5) * (√7-√5)/(√7-√5) = (√7-√5)/(7 - 5) = (√7-√5)/2

Now our expression simplifies to:
(5+√7)/2 + (7-√5)/2 - (√7-√5)/2

Combine the terms with the same denominator:
[(5+√7) + (7-√5) - (√7-√5)] / 2
(5 + √7 + 7 - √5 - √7 + √5) / 2
(12) / 2
6

Therefore, the simplified expression is 6.