expressing P(x) = ((x^2 + x)/((x−3)(x^2 −2))) in partial fractions gives A. (A/((x−3))) + ((Bx + C)/((x^2 −2))) B. (A/(x−3)) + (B/(x−2)) + (C/(x+2)) C. (A/(x−3)) + (B/(x−(√2))) + (C/(x + (√2))) D. ((Ax + B)/(x−3)) + (C/(x^2 −2))


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Question Number 78075 by Rio Michael last updated on 14/Jan/20
$expressing P(x) = ((x^2 + x)/((x−3)(x^2 −2))) in partial fractions gives A. (A/((x−3))) + ((Bx + C)/((x^2 −2))) B. (A/(x−3)) + (B/(x−2)) + (C/(x+2)) C. (A/(x−3)) + (B/(x−(√2))) + (C/(x + (√2))) D. ((Ax + B)/(x−3)) + (C/(x^2 −2))$
$${expressing}\:\:{P}\left({x}\right)\:=\:\frac{{x}^{\mathrm{2}} \:+\:{x}}{\left({x}−\mathrm{3}\right)\left({x}^{\mathrm{2}} −\mathrm{2}\right)}\:{in}\:{partial}\:{fractions}\:{gives} \\ $$$${A}.\:\:\frac{{A}}{\left({x}−\mathrm{3}\right)}\:+\:\frac{{Bx}\:+\:{C}}{\left({x}^{\mathrm{2}} −\mathrm{2}\right)}\: \\ $$$${B}.\:\:\frac{{A}}{{x}−\mathrm{3}}\:+\:\frac{{B}}{{x}−\mathrm{2}}\:+\:\frac{{C}}{{x}+\mathrm{2}} \\ $$$${C}.\:\frac{{A}}{{x}−\mathrm{3}}\:+\:\frac{{B}}{{x}−\sqrt{\mathrm{2}}}\:+\:\frac{{C}}{{x}\:+\:\sqrt{\mathrm{2}}} \\ $$$${D}.\:\frac{{Ax}\:+\:{B}}{{x}−\mathrm{3}}\:+\:\frac{{C}}{{x}^{\mathrm{2}} −\mathrm{2}} \\ $$
Commented by mr W last updated on 14/Jan/20

$${both}\:{A}\:{and}\:{C}\:{are}\:{possible} \\ $$
Commented by mathmax by abdo last updated on 14/Jan/20

$${the}\:{correct}\:{decomposition}\:{is}\:{C} \\ $$
Commented by Rio Michael last updated on 14/Jan/20

$${sirs}\:{is}\:{C}\:{actually}\:{correct}?\: \\ $$$${or}\:{can}\:{i}\:{use}\:{both}\:{A}\:{and}\:{C}\:{as}\:{answers}? \\ $$
Commented by mr W last updated on 14/Jan/20

$${C}\:{is}\:{correct}. \\ $$
Commented by Rio Michael last updated on 14/Jan/20

$${okay}\:{sir}\:{thanks} \\ $$
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