\(a,ĐK:x\ne-1;x\ne-3;x\ne-5;x\ne-7;x\ne-9\\ PT\Leftrightarrow\dfrac{1}{\left(x+1\right)\left(x+3\right)}+\dfrac{1}{\left(x+3\right)\left(x+5\right)}+\dfrac{1}{\left(x+5\right)\left(x+7\right)}+\dfrac{1}{\left(x+7\right)\left(x+9\right)}=\dfrac{1}{5}\\ \Leftrightarrow\dfrac{2}{\left(x+1\right)\left(x+3\right)}+\dfrac{2}{\left(x+3\right)\left(x+5\right)}+\dfrac{2}{\left(x+5\right)\left(x+7\right)}+\dfrac{2}{\left(x+7\right)\left(x+9\right)}=\dfrac{2}{5}\\ \Leftrightarrow\dfrac{1}{x+1}+\dfrac{1}{x+3}-\dfrac{1}{x+3}+\dfrac{1}{x+5}-\dfrac{1}{x+5}+\dfrac{1}{x+7}-\dfrac{1}{x+7}+\dfrac{1}{x+9}=\dfrac{2}{5}\\ \Leftrightarrow\dfrac{1}{x+1}+\dfrac{1}{x+9}=\dfrac{2}{5}\\ \Leftrightarrow5x+45+5x+5=2x^2+20x+18\\ \Leftrightarrow2x^2+10x-32=0\\ \Leftrightarrow x=\dfrac{-5\pm\sqrt{89}}{2}\left(tm\right)\)
