Solve by factorization
X^{2} +(a/a+b + a+b/a)x+1 = 0
X^{2} +(a/a+b + a+b/a)x+1
=> X^{2} +(a/a+b x a+b/ax + a/a+b .a+b/a)
=> X[x+a/a+b] +a+b/a[a+a*a+b]= 0
=> X= -a*a+b x= (-a+b/a) a+b ≠ 0