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\frac{\left(6x^{2}-1\right)\left(2x-2\right)}{3}
Divide 6x^{2}-1 by \frac{3}{2x-2} by multiplying 6x^{2}-1 by the reciprocal of \frac{3}{2x-2}.
\frac{12x^{3}-12x^{2}-2x+2}{3}
Use the distributive property to multiply 6x^{2}-1 by 2x-2.
\frac{\left(6x^{2}-1\right)\left(2x-2\right)}{3}
Divide 6x^{2}-1 by \frac{3}{2x-2} by multiplying 6x^{2}-1 by the reciprocal of \frac{3}{2x-2}.
\frac{12x^{3}-12x^{2}-2x+2}{3}
Use the distributive property to multiply 6x^{2}-1 by 2x-2.