4/(x²-1) can be expressed as 2/(x-1)-2/(x+1) Thus, the given equation becomes: 2/(x-1)-2/(x+1)-(x-1)/(x+1)=(x+7)/(x-1) Bringing terms with same denominator on each side together, we get: 2/(x-1)-(x+7)/(x-1)=2/(x+1)+(x-1)/(x+1) i.e., [2-(x+7)]/(x-1)=[2+(x-1)]/(x+1) (-x-5)/(x-1)=(x+1)/(x+1) -- (i) (i) x is obviously not -1, hence RHS of (i) reduces to 1 i.e., (-x-5)/(x-1)=1 -x-5=x-1 => -2x=4 => x=-2
