Question

Các bạn làm giúp mình bài này . Mình gấp lắm !

Giải phương trình :

\(\dfrac{1}{x\left(x-1\right)}+\dfrac{1}{\left(x-1\right)\left(x-2\right)}+\dfrac{1}{\left(x-2\right)\left(x-3\right)}+\dfrac{1}{\left(x-3\right)\left(x-4\right)}=\dfrac{1}{x-4}+2\)

Answer 1

\(\dfrac{1}{x\left(x-1\right)}+\dfrac{1}{\left(x-1\right)\left(x-2\right)}+...+\dfrac{1}{\left(x-3\right)\left(x-4\right)}=\dfrac{1}{x-4}+2\)

Đk: \(x\ne0;x\ne1;x\ne2;x\ne3;x\ne4\)

\(\Leftrightarrow\dfrac{1}{\left(x-4\right)\left(x-3\right)}+\dfrac{1}{\left(x-3\right)\left(x-2\right)}+...+\dfrac{1}{\left(x-1\right)x}=\dfrac{1}{x-4}+2\)

\(\Leftrightarrow\dfrac{1}{x-4}-\dfrac{1}{x-3}+\dfrac{1}{x-3}-\dfrac{1}{x-2}+...+\dfrac{1}{x-1}-\dfrac{1}{x}=\dfrac{1}{x-4}+2\)

\(\Leftrightarrow\dfrac{1}{x-4}-\dfrac{1}{x}=\dfrac{1}{x-4}+2\)

\(\Leftrightarrow-\dfrac{1}{x}=2\)\(\Leftrightarrow-1=2x\Leftrightarrow x=-\dfrac{1}{2}\)