Question

Chứng minh rằng :

\(\frac{1}{a.\left(a+1\right)}=\frac{1}{a}-\frac{1}{a+1}\)

( a khác 0, a khác -1)

Answer 1

quy đồng mẫu số vế phải là ra mak bạn

Answer 2

\(\text{Ta có: }\)

\(VP=\frac{1}{a.\left(a+1\right)}=\frac{a+1-a}{a.\left(a+1\right)}=\frac{a+1}{a.\left(a+1\right)}-\frac{a}{a.\left(a+1\right)}=\frac{1}{a}-\frac{1}{a+1}=VT\left(đpcm\right)\)

Answer 3

ta có  \(\frac{1}{a}-\frac{1}{a+1}=\frac{a+1}{a.\left(a+1\right)}-\frac{a}{a.\left(a+1\right)}\)

=\(\frac{a+1-a}{a.\left(a+1\right)}=\frac{1}{a.\left(a+1\right)}\)

=>\(\frac{1}{a.\left(a+1\right)}=\frac{1}{a}-\frac{1}{a+1}\left(dpcm\right)\)