\(\frac{2}{\left(x+3\right)\left(x+1\right)}+\frac{2}{\left(x+3\right)\left(x+5\right)}+\frac{2}{\left(x+5\right)\left(x+7\right)}=\frac{2}{9}\)
\(\Rightarrow\frac{2}{x+1}-\frac{2}{x+3}+\frac{2}{x+3}-\frac{2}{x+5}+\frac{2}{x+5}-\frac{2}{x+7}=\frac{2}{9}\)
\(\frac{2}{x+1}-\frac{2}{x+7}=\frac{2}{9}\\ \Rightarrow\frac{2x+14-2x-2}{\left(x+1\right)\left(x+7\right)}=\frac{2}{9}\\ \Rightarrow\frac{12}{\left(x+1\right)\left(x+7\right)}=\frac{2}{9}=\frac{12}{54}\)
\(\Rightarrow\left(x+1\right)\left(x+7\right)=54\\ \Rightarrow x^2+8x-54=0\Rightarrow x=-4\pm\sqrt{70}\)
chết oy mk nhầm nha
\(\Rightarrow\frac{2}{\left(x+1\right)\left(x+3\right)}+\frac{2}{\left(x+3\right)\left(x+5\right)}+\frac{2}{\left(x+5\right)\left(x+7\right)}=\frac{2}{9}\Leftrightarrow\frac{1}{x+1}-\frac{1}{x+7}=\frac{2}{9}\)
\(\Rightarrow\frac{6}{\left(x+1\right)\left(x+7\right)}=\frac{2}{9}=\frac{6}{27}\\ \Rightarrow\left(x+1\right)\left(x+7\right)=27\)
\(\Rightarrow x^2+8x-20=0\Rightarrow\left(x-2\right)\left(x+10\right)=0\Rightarrow\orbr{\begin{cases}x=2\\x=-10\end{cases}}\)
sorry bạn nha mk nhầm xíu
