1) prove that a³+2a/(a⁴+3a²+1)
is reducible
solution
The fraction is reduciblevif and only if its reciprocral is reducible
its reciprocal is
(a⁴+3a²+1)/a³+2a = a + (a²+1)/a³+2a
simplyfying the problem to provide irreducibility of
(a²+1)/a³+2a
which is reducible if and only if
a³+2a/(a²+1)
Continuing the process again and again we come to the point
1/a which is irreducble
hence proved.
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