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Simplify the expression $\frac{x^2+2x+4}{\left(x+1\right)^3}$

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Final Answer

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Limit

$\lim_{x\to-1}\left(\frac{x^2+2x+4}{\left(x+1\right)^3}\right)=\mathrm{The\:limit\:does\:not\:exist}$ See full solution

Derivative

$\frac{d}{dx}\left(\frac{x^2+2x+4}{\left(x+1\right)^3}\right)=\frac{\left(2x+2\right)\left(x+1\right)^3+3\left(-x^2-2x-4\right)\left(x+1\right)^{2}}{\left(x+1\right)^{6}}$ See full solution

Integral

$\int\frac{x^2+2x+4}{\left(x+1\right)^3}dx=\frac{-1}{\left(x+1\right)^{2}}+\frac{1}{-2\left(x+1\right)^{2}}+\frac{2}{x+1}+\ln\left(x+1\right)+\frac{-2}{x+1}+C_0$ See full solution

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Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

SimplifyWrite in simplest formFactorFactor by completing the squareFind the integralFind the derivativeFind (x^2+2x)/((x+1)^3) using the definitionSolve by quadratic formula (general formula)Find the rootsFind break even pointsFind the discriminant

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Main Topic: Simplification of algebraic fractions

Simplification or reduction of algebraic fractions is the action of dividing the numerator and denominator of a fraction by a common factor in order to obtain another much simpler equivalent fraction. We can say that a fraction is reduced to its simplest when there is no common factor between the numerator and the denominator.

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