#### Answer

$\dfrac{x+4}{x^{2}+12x+20}+\dfrac{x+1}{x^{2}+8x-20}=\dfrac{2x^{2}+5x-6}{(x+10)(x+2)(x-2)}$

#### Work Step by Step

$\dfrac{x+4}{x^{2}+12x+20}+\dfrac{x+1}{x^{2}+8x-20}$
Factor the denominator of both rational expressions:
$\dfrac{x+4}{(x+10)(x+2)}+\dfrac{x+1}{(x+10)(x-2)}=...$
Evaluate the sum of the two rational expressions and simplify:
$...=\dfrac{(x+4)(x-2)+(x+1)(x+2)}{(x+10)(x+2)(x-2)}=...$
$...=\dfrac{x^{2}+2x-8+x^{2}+3x+2}{(x+10)(x+2)(x-2)}=\dfrac{2x^{2}+5x-6}{(x+10)(x+2)(x-2)}$