Question

chứng minh các đẳng thức sau:

a, 1/ a*(a+1)=1/a-1/a+1

b, 2/a*(a+1)*(a+2)=1/a*(a+1)-1/(a+1)*(a+2)

giúp mình nhé

mình cần gấp

 

Answer 1

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

b) \(\frac{2}{a\left(a+1\right)\left(a+2\right)}=\frac{\left(a+2\right)-a}{a\left(a+1\right)\left(a+2\right)}=\frac{a+2}{a\left(a+1\right)\left(a+2\right)}-\frac{a}{a\left(a+1\right)\left(a+2\right)}\)

\(=\frac{1}{a\left(a+1\right)}-\frac{1}{\left(a+1\right)\left(a+2\right)}\)

Answer 2

a, Ta có : \(\frac{1}{a}-\frac{1}{a+1}=\frac{a+1}{a\left(a+1\right)}-\frac{a}{a\left(a+1\right)}=\frac{a+1-a}{a\left(a+1\right)}\)

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

b, Ta có : \(\frac{1}{a\left(a+1\right)}-\frac{1}{\left(a+1\right)\left(a+2\right)}=\frac{a+2}{a\left(a+1\right)\left(a+2\right)}-\frac{a}{a\left(a+1\right)\left(a+2\right)}\)

\(VT=\frac{2}{a\left(a+1\right)\left(a+2\right)}\left(đpcm\right)\)