# How do you write the partial fraction decomposition of the rational expression #(7 x^2 - 7 x+12)/(x^4+x^2-2)#?

##### 1 Answer

#### Explanation:

From the given, we start from the factoring part of the denominator

so that

and

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

it follows

Solve A using first equation

Solve B using second equation

the final answer

God bless...I hope the explanation is useful..