$\text{$\dfrac{x+1}{2x+6}$+$\dfrac{2x+3}{x²+3x}$}$ $\text{=$\dfrac{x+1}{2(x+3)}$+$\dfrac{2x+3}{x(x+3)}$}$ $\text{=$\dfrac{x²+x}{2x(x+3)}$+$\dfrac{4x+6}{2x(x+3)}$}$ $\text{=$\dfrac{x²+5x+6}{2x(x+3)}$}$ $\text{=$\dfrac{(x+2)(x+3)}{2x(x+3)}$}$ $\text{=$\dfrac{x+2}{2x}$}$
(x+1)/(2x+6)+(2x+3)/(x^2+3x)(x ne0;xne-3) =(x+1)/(2(x+3))+(2x+3)/(x(x+3)) =(x(x+1)+2(2x+3))/(2x(x+3)) =(x^2+5x+6)/(2x(x+3)) =((x+2)(x+3))/(2x(x+3)) =(x+2)/(2x)
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