Question

\(\dfrac{1}{\left(x+1\right)\left(x+4\right)}\)+\(\dfrac{1}{\left(x+4\right)\left(x+7\right)}\)+\(\dfrac{1}{\left(x+7\right)\left(x+10\right)}\)+\(\dfrac{1}{\left(x+10\right)\left(x+13\right)}\)=\(\dfrac{4}{13}\)

Answer 1

\(\Leftrightarrow\dfrac{3}{\left(x+1\right)\left(x+4\right)}+\dfrac{3}{\left(x+4\right)\left(x+7\right)}+\dfrac{3}{\left(x+7\right)\left(x+10\right)}+\dfrac{3}{\left(x+10\right)\left(x+13\right)}=\dfrac{12}{13}\)

\(\Leftrightarrow\dfrac{1}{x+1}-\dfrac{1}{x+13}=\dfrac{12}{13}\)

\(\Leftrightarrow12\left(x+1\right)\left(x+13\right)=13\left(x+13\right)-13\left(x+1\right)=156\)

\(\Leftrightarrow\left(x+1\right)\left(x+13\right)=13\)

\(\Leftrightarrow x^2+14x=0\)

=>x=0 hoặc x=-14