Question

giải phương trình

\(\dfrac{2}{x+1}\)- \(\dfrac{1}{x-2}\)= \(\dfrac{3x-11}{\left(x+1\right)\left(x-2\right)}\)

Answer 1

\(\dfrac{2}{x+1}-\dfrac{1}{x-2}=\dfrac{3x-11}{\left(x+1\right)\left(x-2\right)}\\ ĐKXĐ:x\ne-1;x\ne2\\ \dfrac{2}{x+1}-\dfrac{1}{x-2}=\dfrac{3x-11}{\left(x+1\right)\left(x-2\right)}\\ \Leftrightarrow\dfrac{2\left(x-2\right)}{\left(x+1\right)\left(x-2\right)}-\dfrac{1\left(x+1\right)}{\left(x-2\right)\left(x+1\right)}=\dfrac{3x-11}{\left(x+1\right)\left(x-2\right)}\\ \Rightarrow2x-4-x-1=3x-11\\ \Leftrightarrow2x-x-3x=-11+4+1\\ \Leftrightarrow-2x=-6\\ \Leftrightarrow x=3\left(tm\right)\)

Vậy \(S=\left\{3\right\}\)

Answer 2

=>2x-4-x-1=3x-11

=>3x-11=x-5

=>2x=6

=>x=3