contestada

Write out the form of the partial fraction decomposition of the fraction. Do not determine the numerical values of the coefficients.

[tex]\frac{x^4}{(x^3+x)(x^2-x+7)}[/tex]

Respuesta :

Factorizing the denominator gives

[tex]\dfrac{x^4}{(x^3+x)(x^2-x+7)} = \dfrac{x^4}{x(x^2+1)(x^2-x+7)} = \dfrac{x^3}{(x^2+1)(x^2-x+7)}[/tex]

Then the partial fraction decomposition would take the form

[tex]\dfrac{x^4}{(x^3+x)(x^2-x+7)} = \dfrac{a_0x + b_0}{x^2+1} + \dfrac{a_1x + b_1}{x^2-x+7}[/tex]

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