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Question Number 208866 by Adeyemi889 last updated on 26/Jun/24

Commented by Adeyemi889 last updated on 26/Jun/24

$$partialF\mathit{R}\mathit{a}\mathit{c}\mathit{t}\mathit{i}\mathit{o}\mathit{n}$$$$$$

Answered by Sutrisno last updated on 26/Jun/24

$$=\frac{x^5+4x^3}{x^4-2x^3+3x^2-4x+2}$$$$=x+2+\frac{5x^3-2x^2+6x-4}{(x^2+2){(x-1)}^2}$$$$\frac{5x^3-2x^2+6x-4}{(x^2+2){(x-1)}^2}=\frac{ax+b}{x^2+2}+\frac{c}{x-1}+\frac{d}{{(x-1)}^2}$$$$5x^3-2x^2+6x-4=(ax+b){(x-1)}^2+c(x^2+2)(x-1)+d(x^2+2)$$$$\bullet x=1$$$$d=\frac{5}{3}$$$$\bullet x=0$$$$b-2c+2d=-4$$$$\bullet x=-1$$$$-4a+4b-6c+3d=-17$$$$\bullet x=2$$$$2a+b+6c+6d=40$$$$didapat:a=\frac{4}{9},b=\frac{16}{9},c=\frac{41}{9}$$$$fraksi:$$$$x+2+\frac{4x+16}{9(x^2+2)}+\frac{41}{9(x-1)}+\frac{5}{3{(x-1)}^2}$$$$$$

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