Which expression is equivalent to (√7−1) / (1+√7)?

Question: Which expression is equivalent to (√7−1) / (1+√7)?

A) (4−√7) / 3

B) (4−√7)/ 24

C) (25−√7)/ 24

D) None of these

To simplify the expression (√7−1) / (1+√7), we can multiply the numerator and denominator by the conjugate of the denominator, which is (1-√7). This gives us:

(√7−1) / (1+√7) * (1-√7) / (1-√7) = ((√7−1) * (1-√7)) / (1-7) = (1-2√7+7) / (-6) = (8-2√7) / 6 = (4-√7) / 3

Therefore, the expression (√7−1) / (1+√7) is equivalent to (4-√7) / 3, which is option A.

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