Question

Resolve $\frac{11-2x}{x^2+9x+14}$ partial fractions.

Answer 1

$x^2+9x+14$
$x^2+7x+2x+14$
$(x+7)(x+2)$
$\therefore$ $\frac{11-2x}{x^2+9x+14}=\frac{11-2x}{(x+7)(x+2)}$
Let $\frac{11-2x}{(x+7)(x+2)}=\frac{A}{x+7}+\frac{B}{x+2}$
$=\frac{A(x+2)+B(x+7)}{(x+7)(x+2)}$
$11-2x=A(x+2)+B(x+7)$
$11-2x=Ax+2A+Bx+7B$
Comparing the coefficients of $x$ and constant terms on both side
$A+B=-\mathrm{2.........}\left(1\right)$
$2A+7B=\mathrm{11.....}\left(2\right)$
SImplifying Equations (1) and (2) we get
$2A+2B=-4$
$2A+7B=11$
------------------------
$-5B=-15$
$B=3$
$A+3=-2$
$A=-2-3$
$A=-5$
Putting the value of $A$ and $B$
$\frac{11-2x}{x^2+9x+14}=\frac{-5}{x+7}+\frac{3}{x+2}$