Question

Thực hiện các phép tính sau:

a,(\(\dfrac{x}{x+1}\)+\(\dfrac{x-1}{x}\)):(\(\dfrac{x}{x+1}\)-\(\dfrac{x-1}{x}\))

b,(1+\(\dfrac{x}{y}\)+\(\dfrac{x^2}{y^2}\)).(1-\(\dfrac{x}{y}\)).\(\dfrac{y^2}{x^3-y^3}\)

Answer 1

\(\left(\dfrac{x}{x+1}+\dfrac{x-1}{x}\right):\left(\dfrac{x}{x+1}-\dfrac{x-1}{x}\right)\) \(\left(đk:x\ne0;-1\right)\)

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

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

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