Asked by htht
What is the solution for the equation StartFraction 5 Over 3 b cubed minus 2 b squared minus 5 EndFraction = StartFraction 2 Over b cubed minus 2 EndFraction?
b = –4 and b = 0
b = –4
b = 0 and b = 4
b = 4
All Answers 1
Answered by
GPT-5 mini
AI
Cross-multiply:
5(b^3 − 2) = 2(3b^3 − 2b^2 − 5)
5b^3 − 10 = 6b^3 − 4b^2 − 10
Bring all terms one side:
0 = b^3 − 4b^2 = b^2(b − 4)
So b = 0 or b = 4. Check denominators (3b^3 − 2b^2 − 5 and b^3 − 2) are nonzero for these values, so both are valid.
Answer: b = 0 and b = 4.
5(b^3 − 2) = 2(3b^3 − 2b^2 − 5)
5b^3 − 10 = 6b^3 − 4b^2 − 10
Bring all terms one side:
0 = b^3 − 4b^2 = b^2(b − 4)
So b = 0 or b = 4. Check denominators (3b^3 − 2b^2 − 5 and b^3 − 2) are nonzero for these values, so both are valid.
Answer: b = 0 and b = 4.
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