Let

Put

A(x+1)(x²+1)+B(x²+1)+(Cx+D)(x+1)²=1

Put x+1=0

X=-1

A(0)+B(1+1)+0=1

By equating the coefficient of x² and constant term, A+C=0

A+B+2C=0……(2)

A+B+D=1

Solving (2) and (3),we get,