\(\frac{1}{\left(x+1\right)\left(x+2\right)}+\frac{1}{\left(x+2\right)\left(x+3\right)}+\frac{1}{\left(x+3\right)\left(x+4\right)}\) = \(\frac{1}{x+1}-\frac{1}{x+2}+\frac{1}{x+2}-\frac{1}{x+3}+\frac{1}{x+3}-\frac{1}{x+4}\)
=\(\frac{1}{x+1}-\frac{1}{x+4}\)=\(\frac{1}{10}\)
\(\Rightarrow\frac{3}{\left(x+1\right)\left(x+4\right)}=\frac{1}{10}\) \(\Rightarrow x^2+5x+4=30\)
còn lại bn tự làm
\(\Leftrightarrow x^2+5x-26=0\)
=>5^2-(-4(1.26))=129
=>\(x_{1,2}=\frac{-b+-\sqrt{D}}{2a}=\frac{-5+-\sqrt{129}}{2}\)
=>\(x=+-\frac{\sqrt{129}}{2}-2\frac{1}{2}\)