First Principles AI

Accedmychevron_right11thchevron_rightmathchevron_rightPartial Fractionschevron_rightExercise 5.1

Solution

First factor:

(x+1)(x^2+5x+6)=(x+1)(x+2)(x+3)

Let:

\frac{x^2+4x+5}{(x+1)(x+2)(x+3)}=\frac{A}{x+1}+\frac{B}{x+2}+\frac{C}{x+3}

Solving gives $A=1$ , $B=-1$ , $C=1$ .

\boxed{\frac{x^2+4x+5}{(x+1)(x^2+5x+6)}=\frac{1}{x+1}-\frac{1}{x+2}+\frac{1}{x+3}}