How do you write the partial fraction decomposition of the rational expression #(7 x^2 - 7 x+12)/(x^4+x^2-2)#?
From the given, we start from the factoring part of the denominator
Let us now form the equations using the LCD we continue
Expand and then simplify
Equate now the numerical coefficients of the numerators of left and right sides of the equation
4 equations with 4 unknowns, solve the unknowns A,B,C,D by elimination of variables
by adding first and third equations the result will be
by adding second and fourth equations the result will be
by adding the fifth and sixth equations, the result will be
Solve A using first equation
Solve B using second equation
the final answer
God bless...I hope the explanation is useful..