-5 phan14 và 30 phân -84 có bằng nhau không tại sao

chào anh coolkid em xin phép giải

ta nhân 17 với vế trái ta có:

\(17VT=17\cdot\frac{\left(17^{18}+1\right)}{17^{19}+1}\)

\(17VT=\frac{17^{19}+17}{17^{19}+1}\)

\(17VT=\frac{\left(17^{19}+1\right)+16}{17^{19}+1}\)

=> \(17VT=1+\frac{16}{17^{19}+1}\)

ta rút gọn biểu thức ở vế phải

\(\Rightarrow VP=\frac{\left(17^{18}+17\right)}{17^{19}+17}=\frac{17\cdot\left(17^{17}+1\right)}{17\cdot\left(17^{18}+1\right)}=\frac{17^{17}+1}{17^{18}+1}\)

\(\Rightarrow17VP=17\cdot\frac{17^{17}+1}{17^{18}+1}\)

\(17VP=\frac{\left(17^{18}+17\right)}{17^{18}+1}\)

\(17VP=1+\frac{16}{17^{18}+1}\)

mà ta có \(17^{19}+1>17^{18}+1\)

=> \(\frac{16}{17^{19}+1}<\frac{16}{17^{18}+1}\)

=> \(17VT<17VP\)

=> \(VT<VP\) (đpcm)

* Cách làm : Tử giữ nguyên,còn mẫu ta biến đổi như sau:
Mẫu : ( \(\frac{19}{1}\)+ 1 ) + ( \(\frac{18}{2}\)+ 1 ) + ( \(\frac{17}{3}\)+ 1 ) +...+ ( \(\frac{3}{17}\)+ 1 ) + ( \(\frac{2}{18}\)+ 1 ) + ( \(\frac{1}{19}\)+ 1 ) - 19  ( vì ta cộng với 19 số 1 nên phải trừ 19 )
= \(\frac{20}{1}\)+  \(\frac{20}{2}\)+  \(\frac{20}{3}\)+...+  \(\frac{20}{17}\)+  \(\frac{20}{18}\)+  \(\frac{20}{19}\)- 19
=  \(\frac{20}{2}\)+  \(\frac{20}{3}\)+...+  \(\frac{20}{17}\)+   \(\frac{20}{18}\)+  \(\frac{20}{19}\)+ ( \(\frac{20}{1}\)- 19)
=  \(\frac{20}{2}\)+  \(\frac{20}{3}\)+ ...+   \(\frac{20}{17}\)+  \(\frac{20}{18}\)+  \(\frac{20}{19}\)+  \(\frac{20}{20}\)
= 20.( \(\frac{1}{2}\)+  \(\frac{1}{3}\)+...+  \(\frac{1}{17}\)+  \(\frac{1}{18}\)+  \(\frac{1}{19}\)+  \(\frac{1}{20}\))
=> \(\frac{Tử}{Mâu}\)=  \(\frac{1}{20}\)

Phùng Quang Thịnh biến đổi sai 1 chỗ kìa 

-19 = \(\frac{20}{20}-20\)chứ mà bạn

9999999999999

\(\frac{75}{100}+\frac{18}{21}+\frac{19}{32}+\frac{1}{4}+\frac{3}{21}+\frac{13}{23}\)= \(\frac{1}{3}+\frac{6}{7}+\frac{1}{4}+\frac{1}{7}+\frac{13}{23}+\frac{19}{32}\)

= \(2+\frac{853}{736}=\frac{2325}{736}\)

=\(\frac{2325}{736}\)nhá bạn, nhớ k cho mk đấy nhá, điểm mk đang âm...

Xét tử:

\(\frac{1}{19}+\frac{2}{18}+\frac{3}{17}+....+\frac{19}{1}\)

= \(\left(1+\frac{1}{19}\right)+\left(1+\frac{2}{18}\right)+\left(1+\frac{3}{17}\right)+.....+\left(1+\frac{18}{2}\right)+1\)

= \(\frac{20}{19}+\frac{20}{18}+\frac{20}{17}+.....+\frac{20}{2}+1\)

= \(\frac{20}{20}+\frac{20}{19}+\frac{20}{18}+\frac{20}{17}+...+\frac{20}{2}\)

= \(20\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{20}\right)\)

Thay vào, ta có:

D = \(\frac{20\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{20}\right)}{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{20}}\)

=> D = 20

Tử số = T = \(\frac{1}{19}+\frac{2}{18}+\frac{3}{17}+....+\frac{18}{2}+\frac{19}{1}\) 

\(=\left(\frac{1}{19}+1\right)+\left(\frac{2}{18}+1\right)+\left(\frac{3}{17}+1\right)+....+\left(\frac{19}{1}+1\right)-19\)

\(=\frac{20}{19}+\frac{20}{18}+\frac{20}{17}+....+\frac{20}{2}+20-19\)

\(=\frac{20}{2}+\frac{20}{3}+....+\frac{20}{18}+\frac{20}{19}+\frac{20}{20}\)

\(=20\left(\frac{1}{2}+\frac{1}{3}+....+\frac{1}{18}+\frac{1}{19}+\frac{1}{20}\right)\)

= 20.Mẫu số

\(\Rightarrow\frac{\frac{1}{19}+\frac{2}{18}+....+\frac{18}{2}+\frac{19}{1}}{\frac{1}{2}+\frac{1}{3}+....+\frac{1}{19}+\frac{1}{20}}=20\)

sao cuối lại - đi 19 vậy bạn