Question

Chứng tỏ rằng:

\(\frac{1}{a}\) = \(\frac{1}{a+1}\)+ \(\frac{1}{a\left(a+1\right)}\) với a thuộc Z; a không bằng 0; a không bằng -1

Answer 1

Ta có : \(\frac{1}{a+1}+\frac{1}{a\left(a+1\right)}=\frac{a}{a\left(a+1\right)}+\frac{1}{a\left(a+1\right)}=\frac{a+1}{a\left(a+1\right)}=\frac{1}{a}\)  Với mọi a

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

Answer 2

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

Vậy....