If x is not equal to -1/2, then 6x^3+3 x^2-8x-4/2x+1=

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3x^2 - 4 We group the numerator into two pairs to set up factoring. 6x^3 + 3x^2 - 8x - 4 = 3x^2(2x+1) - 4(2x+1) We factor out the common binomial from each group. 3x^2(2x+1) - 4(2x+1) = (2x+1)(3x^2 - 4) We remove the common factor since 2x+1 is nonzero under the given condition. (2x+1)(3x^2 - 4)(2x+1) = 3x^2 - 4

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$We group the numerator into two pairs to set up factoring.$	$6 x^{3} + 3 x^{2} - 8 x - 4 = 3 x^{2} (2 x + 1) - 4 (2 x + 1)$
$We factor out the common binomial from each group.$	$3 x^{2} (2 x + 1) - 4 (2 x + 1) = (2 x + 1) (3 x^{2} - 4)$
$We remove the common factor since 2 x + 1 is nonzero under the given condition.$	$\frac{( 2 x + 1 ) ( 3 x ^{2} - 4 )}{( 2 x + 1 )} = 3 x^{2} - 4$

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