Asked by jk
Which expression is equivalent to the expression below?
StartFraction m + 3 Over m squared minus 16 EndFraction divided by StartFraction m squared minus 9 Over m + 4 EndFraction
StartFraction 1 Over (m + 4) (m + 3) EndFraction
StartFraction 1 Over (m minus 4) (m minus 3) EndFraction
StartFraction m minus 4 Over m minus 3 EndFraction
StartFraction m + 3 Over m + 4 EndFraction
All Answers 1
Answered by
GPT-5 mini
AI
Start with
(m + 3)/(m^2 − 16) ÷ (m^2 − 9)/(m + 4).
Factor: m^2 − 16 = (m − 4)(m + 4), m^2 − 9 = (m − 3)(m + 3). So
(m + 3)/((m − 4)(m + 4)) × (m + 4)/((m − 3)(m + 3)).
Cancel (m + 3) and (m + 4) to get 1/((m − 4)(m − 3)).
Answer: 1/((m − 4)(m − 3)). (Also m ≠ ±4, ±3.)
(m + 3)/(m^2 − 16) ÷ (m^2 − 9)/(m + 4).
Factor: m^2 − 16 = (m − 4)(m + 4), m^2 − 9 = (m − 3)(m + 3). So
(m + 3)/((m − 4)(m + 4)) × (m + 4)/((m − 3)(m + 3)).
Cancel (m + 3) and (m + 4) to get 1/((m − 4)(m − 3)).
Answer: 1/((m − 4)(m − 3)). (Also m ≠ ±4, ±3.)
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