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express-4t-2-28-t-4-t-2-6-as-a-partial-fraction-




Question Number 33899 by mondodotto@gmail.com last updated on 27/Apr/18
express ((4t^2 −28)/(t^4 +t^2 −6)) as a partial fraction.
express4t228t4+t26asapartialfraction.
Answered by MJS last updated on 27/Apr/18
t^4 +t^2 −6=0  t^2 =−(1/2)±(√((1/4)+6))=−(1/2)±(5/2)= −3 ∨ 2  t^4 +t^2 −6=(t^2 +3)(t^2 −2)  ((4t^2 −28)/(t^4 +t^2 −6))=(A/(t^2 +3))+(B/(t^2 −2))=((A(t^2 −2)+B(t^2 +3))/(t^4 +t^2 −6))  (A+B)t^2 +(−2A+3B)=4t^2 −28  A+B=4 ∧ −2A+3B=−28  A=4−B  −2(4−B)+3B=−28  B=−4  A=8  ((4t^2 −28)/(t^4 +t^2 −6))=(8/(t^2 +3))−(4/(t^2 −2))
t4+t26=0t2=12±14+6=12±52=32t4+t26=(t2+3)(t22)4t228t4+t26=At2+3+Bt22=A(t22)+B(t2+3)t4+t26(A+B)t2+(2A+3B)=4t228A+B=42A+3B=28A=4B2(4B)+3B=28B=4A=84t228t4+t26=8t2+34t22
Commented by math1967 last updated on 27/Apr/18
I can also write  A(t^2 −2)+B(t^2 +3)=4t^2 −28  putting t^2 =2  A×0+B×5=4×2−28  ∴B=−4 similarly we get A=8
IcanalsowriteA(t22)+B(t2+3)=4t228puttingt2=2A×0+B×5=4×228B=4similarlywegetA=8
Answered by math1967 last updated on 27/Apr/18
((8(t^2 −2)−4(t^2 +3))/((t^2 −2)(t^2 +3)))  (8/(t^2 +3)) −(4/(t^2 −2))
8(t22)4(t2+3)(t22)(t2+3)8t2+34t22

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