16Hit1600
Advanced MathHardMultiplying rational expressions

Advanced Math practice question

For x ≠ −1 and x ≠ 2, which expression is equivalent to (x / (x + 1)) · ((x + 1) / (x − 2))?

  1. A. x / (x − 2)Correct
  2. B. x² / ((x + 1)(x − 2))
  3. C. (x + 1) / (x − 2)
  4. D. x / (x + 1)

Answer: A. x / (x − 2)

Multiply straight across and cancel the common factor (x + 1) from the numerator of one fraction and the denominator of the other: x / (x − 2).

Why the other answers are wrong

B. x² / ((x + 1)(x − 2))
This multiplied the denominators but dropped the (x + 1) in the numerator of the second fraction. Both numerators multiply too, and then (x + 1) cancels.
C. (x + 1) / (x − 2)
The x from the first numerator was lost. After cancelling (x + 1), the numerator is x.
D. x / (x + 1)
This is just the first fraction. Multiplying by (x + 1)/(x − 2) changes the denominator to (x − 2).

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