How do you express 7x2(x3)2(x+1) in partial fractions?

1 Answer
Feb 11, 2017

The answer is =194(x3)2+916x3+916x+1

Explanation:

Let's perform the decomposition into partial fractions

7x2(x3)2(x+1)=A(x3)2+Bx3+Cx+1

=A(x+1)+B((x3)(x+1))+C(x3)2(x3)2(x+1)

The denominators are the same, we compare the numerators

7x2=A(x+1)+B((x3)(x+1))+C(x3)2

Let x=3, , 19=4A, , A=194

Let x=1, , 9=16C, , C=916

Coefficients of x2

0=B+C, , B=C=916

Therefore,

7x2(x3)2(x+1)=194(x3)2+916x3+916x+1