Advanced Math practice question

Answer: A. x/2

Dividing by a fraction is multiplying by its reciprocal: 3/(x + 1) · (x² + x)/6. Factor x² + x = x(x + 1); the (x + 1) cancels and 3/6 = 1/2, leaving x/2.

Why the other answers are wrong

B. 2/x

2/x is the reciprocal of the answer — the division was set up the wrong way round.

C. x/(2(x + 1))

x/(2(x + 1)) forgets that the (x + 1) in the first denominator cancels with the (x + 1) inside x² + x.

D. (x + 1)/2

(x + 1)/2 cancels the x instead of the (x + 1): x² + x = x(x + 1), and it is the (x + 1) that matches the denominator.

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