Rút gọn

To simplify the expression, let's rationalize the denominators.

For the first fraction, we have:
(căn 2 + căn (4 + căn 7)) * (căn 2 - căn (4 + căn 7))
= (căn 2)^2 - (căn (4 + căn 7))^2
= 2 - (4 + căn 7)
= -2 - căn 7

For the second fraction, we have:
(căn 2 - căn (4 - căn 7)) * (căn 2 + căn (4 - căn 7))
= (căn 2)^2 - (căn (4 - căn 7))^2
= 2 - (4 - căn 7)
= -2 + căn 7

Now we can rewrite the expression as:
(1 + căn 7) / (-2 - căn 7) + (1 - căn 7) / (-2 + căn 7)

To add these fractions, we need a common denominator. The common denominator is (-2 - căn 7)(-2 + căn 7) = 4 - 7 = -3.

Now we can rewrite the expression with the common denominator:
[(1 + căn 7)(-2 + căn 7)] / (-3) + [(1 - căn 7)(-2 - căn 7)] / (-3)

Expanding the numerators, we get:
[-2 + căn 7 - 2căn 7 + 7] / (-3) + [-2 - căn 7 + 2căn 7 + 7] / (-3)

Simplifying the numerators, we get:
[5 - căn 7 - 2căn 7] / (-3) + [5 + căn 7 + 2căn 7] / (-3)

Combining like terms, we get:
[5 - 3căn 7] / (-3) + [5 + 3căn 7] / (-3)

Now we can add the fractions:
[5 - 3căn 7 + 5 + 3căn 7] / (-3)
= 10 / (-3)
= -10/3

Therefore, the simplified expression is -10/3.