Sum of roots of polynomial

Algebra Level 5

Consider the polynomial p(x)p(x) defined as:- p(x)=x4+x3+2x2+3x+1p(x)=x^4+x^3+2x^2+3x+1 Let r1,r2,r3,r4r_1,r_2,r_3,r_4 be the roots of p(x)p(x) then the value of (ij1(1ri)(1rj))(i=1411ri) \left( \sum_{i \neq j} \frac{1}{ (1-r_i)(1-r_j) } \right) \left(\sum_{i=1}^4 \frac{1}{1-r_i} \right) can be expressed as ab\frac{a}{b} where gcd(a,b)=1gcd(a,b)=1 find a+ba+b

Details and assumptions:- I have used the notation (1(1ri)(1rj)\sum(\frac{1}{(1-r_i)(1-r_j)} to represent the sum of all possible products of the form 1(1ri)(1rj)\frac{1}{(1-r_i)(1-r_j)} taken two at a time and iji \neq j (i think it also called cyclic sum)

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