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Question

$open curly brackets x element of R colon fraction numerator 2 x minus 1 over denominator x to the power of 3 end exponent plus 4 x to the power of 2 end exponent plus 3 x end fraction element of R close curly brackets$ equals

$R - {0}$
$R - {0, 1, 3}$
$R - {0, - 1, - 3}$
$R - \{0, - 1, - 3, + \frac{1}{2}\}$

The correct answer is: $R minus left curly bracket 0 comma blank minus 1 comma blank minus 3 right curly bracket$

Let $A equals open curly brackets x element of R colon fraction numerator 2 x minus 1 over denominator x to the power of 3 end exponent plus 4 x to the power of 2 end exponent plus 3 x end fraction close curly brackets$
Now, $x to the power of 3 end exponent plus 4 x to the power of 2 end exponent plus 3 x equals x left parenthesis x to the power of 2 end exponent plus 4 x plus 3 right parenthesis$
$equals x open parentheses x plus 3 close parentheses left parenthesis x plus 1 right parenthesis$
$therefore blank A equals R minus open curly brackets 0 comma blank minus 1 comma blank minus 3 close curly brackets$

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