Advanced Math practice question

Answer: A. (4x + 5)/((x + 2)(x − 1))

Common denominator (x + 2)(x − 1). Numerators: 1(x − 1) + 3(x + 2) = x − 1 + 3x + 6 = 4x + 5.

Why the other answers are wrong

B. 4/((x + 2)(x − 1))

4 adds the numerators without scaling them by the other denominator first.

C. (4x + 7)/((x + 2)(x − 1))

4x + 7 comes from 3(x + 2) = 3x + 6 added to x + 1; the first numerator is x − 1, not x + 1.

D. 4/(2x + 1)

4/(2x + 1) adds numerators and adds denominators, which is never how fractions combine.

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