Algebra: A Combined Approach (4th Edition)

$\dfrac{x+4}{x^{2}+12x+20}+\dfrac{x+1}{x^{2}+8x-20}=\dfrac{2x^{2}+5x-6}{(x+10)(x+2)(x-2)}$
$\dfrac{x+4}{x^{2}+12x+20}+\dfrac{x+1}{x^{2}+8x-20}$ 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: $...=\dfrac{(x+4)(x-2)+(x+1)(x+2)}{(x+10)(x+2)(x-2)}=...$ $...=\dfrac{x^{2}+2x-8+x^{2}+3x+2}{(x+10)(x+2)(x-2)}=\dfrac{2x^{2}+5x-6}{(x+10)(x+2)(x-2)}$