Evaluate
\frac{2x^{2}+5x+1}{\left(x+1\right)\left(2x+1\right)\left(3x+1\right)}
Expand
\frac{2x^{2}+5x+1}{6x^{3}+11x^{2}+6x+1}
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\frac{2\left(x-\left(-\frac{1}{4}\sqrt{17}-\frac{5}{4}\right)\right)\left(x-\left(\frac{1}{4}\sqrt{17}-\frac{5}{4}\right)\right)\left(x^{2}+x+1\right)}{\left(x+1\right)\left(2x+1\right)\left(3x+1\right)\left(x^{2}+x+1\right)}
Factor the expressions that are not already factored.
\frac{2\left(x-\left(-\frac{1}{4}\sqrt{17}-\frac{5}{4}\right)\right)\left(x-\left(\frac{1}{4}\sqrt{17}-\frac{5}{4}\right)\right)}{\left(x+1\right)\left(2x+1\right)\left(3x+1\right)}
Cancel out x^{2}+x+1 in both numerator and denominator.
\frac{2x^{2}+5x+1}{6x^{3}+11x^{2}+6x+1}
Expand the expression.
\frac{2\left(x-\left(-\frac{1}{4}\sqrt{17}-\frac{5}{4}\right)\right)\left(x-\left(\frac{1}{4}\sqrt{17}-\frac{5}{4}\right)\right)\left(x^{2}+x+1\right)}{\left(x+1\right)\left(2x+1\right)\left(3x+1\right)\left(x^{2}+x+1\right)}
Factor the expressions that are not already factored.
\frac{2\left(x-\left(-\frac{1}{4}\sqrt{17}-\frac{5}{4}\right)\right)\left(x-\left(\frac{1}{4}\sqrt{17}-\frac{5}{4}\right)\right)}{\left(x+1\right)\left(2x+1\right)\left(3x+1\right)}
Cancel out x^{2}+x+1 in both numerator and denominator.
\frac{2x^{2}+5x+1}{6x^{3}+11x^{2}+6x+1}
Expand the expression.
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Limits
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