X^2+7X+4/X^3-X^2-6X + X^2+6X+5/X^2-2X-3
=(2+7√2+4)/(2√2-2-6√2)+(2+6√2+5)/(2-2√2-3)
=(6+7√2)/(-2-4√2)+(7+6√2)/(-1-2√2)
=(6+7√2+14+12√2)/(-2-4√2)
=(20+19√2)/-2(1+2√2)
=(20+19√2)(1-2√2)/-2(1+2√2)(1- 2√2)
=(20+19√21-40√2-76)/-2(-1-8)
=(-56-21√2)/14
=(-8-3√2)/2