9
QuizMultiple Choice

Rational Equations — Quiz

Question 9 • Mathematics III

What is the solution for the equation the fraction with numerator 5 and denominator 3 b cubed minus 2 b squared minus 5 is equal to the fraction with numerator 2 and denominator b cubed minus 2 ?

Answer
A
b is equal to negative 4
B
b is equal to negative 4 and b is equal to 0
C
b is equal to 4
D
b is equal to 0 and b is equal to 4

Explanation

Cross-multiply: 5(b³ − 2) = 2(3b³ − 2b² − 5). Simplifying gives b³ − 4b² = 0, or b²(b − 4) = 0, so b = 0 or b = 4. Neither value makes either denominator zero, so both are valid solutions; the correct choice is “b is equal to 0 and b is equal to 4.”

AI-written and checked against the verified answer.

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