3
QuizMultiple Choice

Rational Equations — Quiz

Question 3 • Mathematics III

Which solution to the equation the fraction with numerator 3 and denominator 2 g plus 8 is equal to the fraction with numerator g plus 2 and denominator g squared minus 16 is extraneous?

Answer
A
g is equal to 16
B
neither g is equal to negative 4 nor g is equal to 16
C
g is equal to negative 4
D
g is equal to negative 4 and g is equal to 16

Explanation

Cross-multiplying gives 3(g² − 16) = (g + 2)(2g + 8), which simplifies to (g − 16)(g + 4) = 0. The resulting candidates are g = 16 and g = −4. But g = −4 makes the original denominators zero, so it is excluded and is the extraneous solution.

AI-written and checked against the verified answer.

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