Answer to Question #114170 in Algebra for Ra

Question

To split (s+10)/((s+4)(s-2)) into two terms.

Answer 1

$\frac{s+10}{(s+4)(s-2)} = \frac{A}{s+4}+\frac{B}{s-2}$

$\frac{s+10}{(s+4)(s-2)} = \frac{A(s-2)+B(s+4)}{(s+4)(s-2)}$

$s+10 = As-2A+Bs+4B$

$A + B = 1$

$4B-2A=10$

$A= 1-B$

$4B-2(1-B)=10$

$4B-2+2B=10$

$6B=12$

$B=2$

$A=1-2=-1$

Answer

$\frac{-1}{s+4}+\frac{2}{s-2}$