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))?
- A. x / (x − 2)Correct
- B. x² / ((x + 1)(x − 2))
- C. (x + 1) / (x − 2)
- 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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