<s>[INST] partial fractions for a function I need help finding the partial fraction decomposition for this function, I am just lost on it, here it is:
$(x^2 + x + 1)/(2x^4+3x^2+1)$. the help is appreciated. thank you.
 [/INST] As suggested by one user.
$\frac{(x^2 + x + 1)}{(2x^4+3x^2+1)} = \frac{ax+b}{2x^2+1} + \frac{cx+d}{x^2+1}$
$x^2+x+1 = (ax+b)(x^2+1) + (cx+d)(2x^2+1)$
Comparing terms containing $x^3$,
$0 = a + 2c$
Comparing terms containing $x^2$,
$1 = b + 2d$
Comparing terms containing $x$,
$1 = a + c$
Comparing terms containing constant terms,
$1 = b + d$
Hope you can solve above equations to find a, b, c and d.
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