Rationalize the denominator and simplify.. help please

Rationalize the denominator and simplify

_____7_____
√7 + 1

7 / [√(7) + 1] = 7[√(7) − 1] / [√(7) + 1][√(7) − 1]
. . . . . . . . . .= 7[√(7) − 1] / (7 - 1)
. . . . . . . . . .= 7[√(7) − 1] / 6

7 (√7 - 1)
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(√ 7 + 1)(√ 7 - 1)

7 (√7 - 1)
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6