Giải:
a) Biến đổi VP, ta có:
\(\dfrac{1}{a}-\dfrac{1}{a+1}\)
\(=\dfrac{1.\left(a+1\right)}{a.\left(a+1\right)}-\dfrac{a.1}{a.\left(a+1\right)}\)
\(=\dfrac{a+1}{a.\left(a+1\right)}-\dfrac{a}{a.\left(a+1\right)}\)
\(=\dfrac{a+1-a}{a.\left(a+1\right)}\)
\(=\dfrac{1}{a.\left(a+1\right)}\) (đpcm)
b) Biến đổi VP, ta được:
\(\dfrac{1}{a\left(a+1\right)}-\dfrac{1}{\left(a+1\right)\left(a+2\right)}\)
\(=\dfrac{1\left(a+2\right)}{a\left(a+1\right)\left(a+2\right)}-\dfrac{1.a}{a\left(a+1\right)\left(a+2\right)}\)
\(=\dfrac{a+2}{a\left(a+1\right)\left(a+2\right)}-\dfrac{a}{a\left(a+1\right)\left(a+2\right)}\)
\(=\dfrac{a+2-a}{a\left(a+1\right)\left(a+2\right)}\)
\(=\dfrac{2}{a\left(a+1\right)\left(a+2\right)}\) (đpcm)
Chúc bạn học tốt!!!