Question

. Thực hiện phép tính sau 

a) 2/x² − 1 + 1/x − 1 + 1/x + 1 .

Answer 1

\(đk:x\ne1;-1\)

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