Question

câu 3:Tính
b) 
với x khác -1 ;x khác 0; x khác 1

Answer 1

\(\dfrac{1}{x^2-x}+\dfrac{x-3}{x^2-1}\left(x\ne\pm1;x\ne0\right)\)

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

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

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

\(=\dfrac{x^2-2x+1}{\left(x-1\right)\left[x\left(x+1\right)\right]}\)

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

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