x/(x2+3x+1)=a (a≠0)find x2/(x4+3x2+1)plzz xplain

Hello student,
Please find the answer to your question below
Givenx/(x2+3x+1)=a
So (1/(x+1/x+3))=a
1/a=3+x+1/x
x+1/x=3-(1/a)
squaring on both sides we get
x²+1/x²=7+(1/a²)-(6/a).................(1)
Asked to findx²/(x⁴+3x²+1)=1/x²+(1/x²)+3
=1/(7-(6/a)+(1/a²)) from (1)
=a²/(7a²-6a+1)