Question

Привет, помогите пожалуйста)

Answer 1

$\displaystyle \tt \frac{2^{21}\cdot27^3+15\cdot4^{10}\cdot9^4}{69\cdot2^{10}+12^{10}}=\frac{2^{21}\cdot3^9+15\cdot2^{20}\cdot3^8}{69\cdot1024+12^{10}}=\frac{2^{20}\cdot3^8\cdot(2\cdot3+15)}{70656+12^{10}}=\frac{2^{20}\cdot3^8\cdot(6+15)}{70656+12^{10}}=\\ =\frac{2^{20}\cdot6561\cdot21}{70656+12^{10}}=\bold{\frac{137781\cdot2^{20}}{70656+12^{10}}}$

$\displaystyle \tt (\frac{1}{a+1}+\frac{1}{a})\div(2a+1)=\frac{a+a+1}{a(a+1)}\cdot\frac{1}{2a+1}=\frac{2a+1}{a(a+1)}\cdot\frac{1}{2a+1}=\frac{1}{a(a+1)}=\\=\bold{\frac{1}{a^2+a}}$

$\displaystyle \tt (\frac{1}{a-1}-\frac{1}{a+1})\div\frac{2}{a-1}=\cdot{\frac{a+1-(a-1)}{(a-1)}(a+1)}\cdot\frac{a-1}{2}=\frac{a+1-a+1}{a+1}\cdot\frac{1}{2}=\frac{2}{a+1}\frac{1}{2}=\bold{\frac{1}{a+1}}$