Asked by jk
Which expression is equivalent to StartFraction c squared minus 4 Over c + 3 EndFraction divided by StartFraction c + 2 Over 3 (c squared minus 9) EndFraction?
StartFraction c + 3 Over c squared minus 4 EndFraction times StartFraction c + 2 Over 3 (c squared minus 9) EndFraction
StartFraction c squared minus 4 Over c + 3 EndFraction divided by StartFraction 3 (c squared minus 9) Over c + 2 EndFraction
StartFraction c squared minus 4 Over c + 3 EndFraction times StartFraction 3 (c squared minus 9) Over c + 2 EndFraction
StartFraction c squared minus 4 Over c + 3 EndFraction times StartFraction c + 2 Over 3 (c squared minus 9) EndFraction
All Answers 1
Answered by
GPT-5 mini
AI
Choose the third expression.
Reason: dividing by a fraction means multiplying by its reciprocal:
(c^2 − 4)/(c + 3) ÷ [(c + 2)/(3(c^2 − 9))] = (c^2 − 4)/(c + 3) · [3(c^2 − 9)/(c + 2)].
You can further factor and simplify:
= [(c − 2)(c + 2)/(c + 3)] · [3(c − 3)(c + 3)/(c + 2)] = 3(c − 2)(c − 3),
with c ≠ −3, −2, 3 (values that make the original expression undefined).
Reason: dividing by a fraction means multiplying by its reciprocal:
(c^2 − 4)/(c + 3) ÷ [(c + 2)/(3(c^2 − 9))] = (c^2 − 4)/(c + 3) · [3(c^2 − 9)/(c + 2)].
You can further factor and simplify:
= [(c − 2)(c + 2)/(c + 3)] · [3(c − 3)(c + 3)/(c + 2)] = 3(c − 2)(c − 3),
with c ≠ −3, −2, 3 (values that make the original expression undefined).
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