Question

thực hiện phép tính:

                             x+1/x-1-x-1/x+1-4/1-x^2

 

Answer 1

\(\frac{x+1}{x-1}-\frac{x-1}{x+1}-\frac{4}{1-x^2}=\frac{\left(x+1\right)^2}{\left(x-1\right)\left(x+1\right)}-\frac{\left(x-1\right)^2}{\left(x+1\right)\left(x-1\right)}+\frac{4}{\left(x-1\right)\left(x+1\right)}\)

\(=\frac{\left(x+1\right)^2-\left(x-1\right)^2-4}{\left(x-1\right)\left(x+1\right)}=\frac{\left(x+1-x+1\right)\left(x+1+x-1\right)-4}{\left(x-1\right)\left(x+1\right)}\)

\(\frac{2.2x-4}{\left(x-1\right)\left(x+1\right)}=\frac{4\left(x-1\right)}{\left(x-1\right)\left(x+1\right)}=\frac{4}{x+1}\)