Question

lf $\frac{1-11x}{(x+1)(x+6)(x-4)}=\frac{A}{x+1}+\frac{B}{x+6}+\frac{C}{x-4}$, then $B$ is equal to

• A. $\frac{-12}{25}$
• B. $\frac{67}{50}$
• C. $\frac{-43}{50}$
• D. $\frac{-67}{50}$

Answer 1

The correct option is B $\frac{67}{50}$

We have $\frac{1-11x}{(x+1)(x+6)(x-4)}=\frac{A}{x+1}+\frac{B}{x+6}+\frac{C}{x-4}$
Multiply on both sides by $(x+1)(x+6)(x-4)$

$1-11x=A(x+6)(x-4)+(x+1)(x-4)B+(x+1)(x+6)C$

Substitute $x=-6$

$1+66=B(1-6)(-6-4)$

Therefore, $B=\frac{67}{50}$