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Question Number 27578 by Mcfaithal last updated on 10/Jan/18

$$\mathrm{if}\mathrm{f}\left(\mathrm{x}\right)=\frac{2\mathrm{x}-3}{({\mathrm{x}}^2-1)(\mathrm{x}+2)}$$$$1.\mathrm{Find}\mathrm{the}\mathrm{value}\mathrm{for}\mathrm{which}\mathrm{f}\left(\mathrm{x}\right)\mathrm{is}\mathrm{undefied}.$$$$2.\mathrm{Express}\mathrm{f}\left(\mathrm{x}\right)\mathrm{in}\mathrm{partial}\mathrm{fraction}$$

Commented by abdo imad last updated on 10/Jan/18

$$D=R-\{1,-1,-2\}$$$$f\left(x\right)=\frac{a}{x-1}+\frac{b}{x+1}+\frac{c}{x+2}$$$$wehavef\left(x\right)=\frac{2x-3}{(x-1)(x+1)(x+2)}$$$$\Rightarrow a=\frac{-1}{6},b=\frac{5}{2},c=\frac{-7}{3}and$$$$f\left(x\right)=\frac{-1}{6(x-1)}+\frac{5}{2(x+1)}-\frac{7}{3(x+2)}.$$

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