Mathematics

Problem

## Explorations 53. Revisiting Example 3 When we cleared fractions in Example 3 we obtained the equation

x^{2}+4 x+1=A\left(x^{2}+1\right)+(B x+C)(x-1)

(a) Substitute

x=1

into this equation and solve for

A

. (b) Substitute

x=i

and

x=-i

into this equation to find a system of 2 equations to solve for

B

and

C