x²+3x+2=(x+1)(x+2)
x²+5x+6=(x+2)(x+3)
x²+6x+5=(x+5)(x+1)
x²+4x+3=(x+1)(x+3)
[tex] \frac{x^+3x+2}{ x^{2} +5x+6}+ \frac{x^2+6x+5}{ x^{2} +4x+3}= \frac{(x+1)(x+2)}{(x+2)(x+3)}+ \frac{(x+1)(x+5)}{(x+1)(x+3)} = \\ = \frac{x+1}{x+3}+ \frac{x+5}{x+3}= \frac{2x+6}{x+3}= \frac{2(x+3)}{x+3} =2 [/tex]
