a/x+b/(7x-3)+(cx+d)/(x^2+1)=(x^3+x^2-x+1)/(x(7x-3)(x^2+1))
a(7x-3)(x^2+1)+bx(x^2+1)+(cx+d)x(7x-3)=x^3+x^2-x+1
a(7x^3-3x^2+7x-3)+b(x^3+x)+7cx^3+(-3c+7d)x^2-3dx=x^3+x^2-x+1
(7a+b+7c)x^3+(-3a-3c+7d)x^2+(7a+b-3d)x+(-3a)=x^3+x^2-x+1
-3a=1 a=-1/3
-7/3+b+7c=1 b+7c=10/3
1-3c+7d=1 c=7d/3
-7/3+b-3d=-1 b-3d=4/3
7c+3d=2 58d=6 d=3/29
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