Question

Chứng minh rằng: \(\dfrac{1}{a}\)= \(\dfrac{1}{a+1}\)+ \(\dfrac{1}{a\left(a+1\right)}\)với a \(\in\) Z; a \(\ne\)0,-1.

Answer 1

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

Suy ra \(\dfrac{1}{a}=\dfrac{1}{a+1}+\dfrac{1}{a\left(a+1\right)}\)

Answer 2

Help me!