=(x^2-xy+3y^2)/(x^2+xy+6y^2)
=(y^2)(x^2/y^2-xy/y^2+3)/[(y^2)(x^2/y^2+xy/y^2+6)]
=(4-2+3)/(4+2+6)
=(5)/( 12)
=5/ 12
Known: x/(x 2+x+1) = a, (x 2+x+1)/x =1/a, x+ 1+x = 65438. =( 1/a- 1)?
x? +2+ 1/x? =( 1/a- 1)? ,x? + 1/x? + 1=( 1/a- 1)? - 1,(x^4+x^2+ 1)/x? =( 1/a)( 1/a-2)
∴x? /(x^4+x^2+ 1)= 1/[ 1/a( 1/a-2)]
x^2/x^4+x^2+ 1
=x^2/(x^4+x^2+ 1)
= 1/[ 1/a( 1/a-2)]