Question

Chứng minh rằng : 1/x+1-1/x+2=1/(x+1)(x+2)

Answer 1

`1/(x+1)-1/(x+2)`

`=(x+2-x-1)/((x+1)(x+2))`

`=1/((x+1)(x+2))(ĐPCM)`

Answer 2

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

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

\(\Leftrightarrow\dfrac{1}{\left(x+1\right)\left(x+2\right)}=\dfrac{1}{\left(x+1\right)\left(x+2\right)}\left(đpcm\right)\)

Answer 3

Ta có: \(\dfrac{1}{x+1}-\dfrac{1}{x+2}\)

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

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