Asked by j
Which expression is equivalent to the expression below?
StartFraction 6 c squared + 3 c Over negative 4 c + 2 EndFraction divided by StartFraction 2 c + 1 Over 4 c minus 2 EndFraction
StartFraction 3 c (2 c minus 1) Over 2 c + 1 EndFraction
StartFraction negative 3 c (2 c + 1) squared Over 4 (2 c minus 1) squared EndFraction
3c
–3c
All Answers 1
Answered by
GPT-5 mini
AI
Simplify stepwise:
(6c^2 + 3c)/(-4c + 2) = 3c(2c + 1)/[-2(2c - 1)] = -3c(2c + 1)/[2(2c - 1)].
Divide by (2c + 1)/(4c - 2) — multiply by the reciprocal:
[-3c(2c + 1)/[2(2c - 1)]] * [(4c - 2)/(2c + 1)].
Cancel (2c + 1) and note 4c - 2 = 2(2c - 1):
[-3c/(2(2c - 1))] * [2(2c - 1)] = -3c.
So the expression is equivalent to -3c (with c ≠ -1/2 and c ≠ 1/2).
(6c^2 + 3c)/(-4c + 2) = 3c(2c + 1)/[-2(2c - 1)] = -3c(2c + 1)/[2(2c - 1)].
Divide by (2c + 1)/(4c - 2) — multiply by the reciprocal:
[-3c(2c + 1)/[2(2c - 1)]] * [(4c - 2)/(2c + 1)].
Cancel (2c + 1) and note 4c - 2 = 2(2c - 1):
[-3c/(2(2c - 1))] * [2(2c - 1)] = -3c.
So the expression is equivalent to -3c (with c ≠ -1/2 and c ≠ 1/2).
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