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\frac{\left(x+1\right)\left(3x+1\right)}{3x+1}\times 4\left(x^{2}-1\right)
Factor the expressions that are not already factored in \frac{3x^{2}+4x+1}{3x+1}.
\left(x+1\right)\times 4\left(x^{2}-1\right)
Cancel out 3x+1 in both numerator and denominator.
\left(4x+4\right)\left(x^{2}-1\right)
Use the distributive property to multiply x+1 by 4.
4x^{3}-4x+4x^{2}-4
Use the distributive property to multiply 4x+4 by x^{2}-1.
\frac{\left(x+1\right)\left(3x+1\right)}{3x+1}\times 4\left(x^{2}-1\right)
Factor the expressions that are not already factored in \frac{3x^{2}+4x+1}{3x+1}.
\left(x+1\right)\times 4\left(x^{2}-1\right)
Cancel out 3x+1 in both numerator and denominator.
\left(4x+4\right)\left(x^{2}-1\right)
Use the distributive property to multiply x+1 by 4.
4x^{3}-4x+4x^{2}-4
Use the distributive property to multiply 4x+4 by x^{2}-1.