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Simplify $\frac{8}{y^2-6y+9}+\frac{4}{y-3}-5$

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Final answer to the problem

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Derivative

$\frac{d}{dy}\left(\frac{8}{y^2-6y+9}+\frac{4}{y-3}-5\right)=\frac{-8\left(2y-6\right)}{\left(y^2-6y+9\right)^2}+\frac{-4}{\left(y-3\right)^2}$ See full solution

Integral

$\int\left(\frac{8}{y^2-6y+9}+\frac{4}{y-3}-5\right)dy=\frac{-8}{y-3}+4\ln\left(y-3\right)-5y+C_0$ See full solution

Explore different ways to solve this problem

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 8/(y^2+-6y)+4/(y-3) using the definitionSolve by quadratic formula (general formula)Find the rootsFind break even pointsFind the discriminant

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Main Topic: Combining like terms

Algebraic expressions can be simplified by combining like terms.

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