\(\frac{121212}{151515}+\frac{121212}{353535}+\frac{121212}{636363}+\frac{121212}{999999}\)

= \(\frac{12.10101}{15.10101}+\frac{12.10101}{35.10101}+\frac{12.10101}{63.10101}+\frac{12.10101}{99.10101}\)

= \(\frac{12}{15}+\frac{12}{35}+\frac{12}{63}+\frac{12}{99}\)

= \(\frac{12}{3.5}+\frac{12}{5.7}+\frac{12}{7.9}+\frac{12}{9.11}\)

= \(6.\left(\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}\right)\)

= \(6.\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}\right)\)

= \(6.\left(\frac{1}{3}-\frac{1}{11}\right)\)

= \(6.\frac{8}{33}\)

= \(\frac{16}{11}\)

2323/202+2323/606+2323/1212+2323/2020+2323/3030+2323/4242+2323/5656+2323/7272+2323/9090.=

\(\frac{23\times101}{2\times101}+\frac{23\times101}{6\times101}+\frac{23\times101}{12\times101}+....+\frac{23\times101}{72\times101}+\frac{23\times101}{90\times101} \)

=\(\frac{23}{2}+\frac{23}{6}+..........+\frac{23}{72}+\frac{23}{90}\)

=\(23\times\left(\frac{1}{1\times2}+\frac{1}{2\times3}+.....+\frac{1}{9\times10}\right)\)

=\(23\times\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{9}-\frac{1}{10}_{ }\right)\)

=\(23\left(1-\frac{1}{10}\right)_{ }\)

=\(23\times\frac{9}{10}\)

==\(\frac{207}{10}\)           

chúc học giỏi nha bn

\(A=\dfrac{121212}{131313}+\dfrac{154154}{143143}-\left(\dfrac{2121}{2323}+\dfrac{275275}{253253}\right)\)

\(=\dfrac{12}{13}+\dfrac{14}{13}-\left(\dfrac{21}{23}+\dfrac{25}{23}\right)\)

\(=2-2=0\)

\(A=\frac{12\cdot10101}{13\cdot10101}+\frac{14\cdot11011}{13\cdot11011}-\left(\frac{21\cdot101}{23\cdot101}+\frac{25\cdot11011}{23\cdot11011}\right)\)

\(A=\frac{12}{13}+\frac{14}{13}-\left(\frac{21}{23}+\frac{25}{23}\right)\)

\(A=0\)

nhớ cho đúng nha

\(A=\frac{121212}{131313}+\frac{154154}{143143}-\left(\frac{2121}{2323}+\frac{275275}{253253}\right)\)

\(\Leftrightarrow A=\frac{12}{13}-\frac{14}{13}-\left(\frac{21}{23}+\frac{25}{23}\right)\) (Áp dụng phương pháp rút gọn phân số)

\(\Leftrightarrow A=\frac{12}{13}-\frac{14}{13}-\frac{46}{23}=\frac{\left(-2\right)}{13}-\frac{46}{23}\)

\(\Leftrightarrow A=-\frac{28}{13}\)

minh ko biet xin loi ban nha!

minh ko biet xin loi ban nha!

minh ko biet xin loi ban nha!

minh ko biet xin loi ban nha!

minh ko biet xin loi ban nha!

Gọi \(\dfrac{12}{23}+\dfrac{12}{2323}-\dfrac{121212}{232323}\) là A

Ta sẽ tính biểu thức A.\(\left(\dfrac{1}{3}+\dfrac{1}{4}-\dfrac{7}{12}\right)\)=A.\(\left(\dfrac{7}{12}-\dfrac{7}{12}\right)=0\)

Vậy \(\left(\dfrac{12}{23}+\dfrac{12}{2323}-\dfrac{121212}{232323}\right).\left(\dfrac{1}{3}+\dfrac{1}{4}-\dfrac{7}{12}\right)\)=0

\(a,-\frac{9}{12}=-\frac{9:3}{12:3}=-\frac{3}{4}\)

\(\frac{-18}{-24}=\frac{\left(-18\right):\left(-6\right)}{\left(-24\right):\left(-6\right)}=\frac{3}{4}\)

\(-\frac{35}{70}=-\frac{35:35}{70:35}=\frac{1}{2}\)

\(-\frac{9}{27}=-\frac{9:9}{27:9}=-\frac{1}{3}\)

\(b,\frac{1313}{4242}=\frac{1313:101}{4242:101}=\frac{13}{42}\)

\(\frac{-353535}{-424242}=\frac{\left(-353535\right):\left(-70707\right)}{\left(-424242\right):\left(-70707\right)}=\frac{5}{6}\)

\(c,\frac{2^3\times4^3\times5^4}{8^2\times25^3\times7}=\frac{2^3\times4^3\times25^2}{8\times8^2\times25^2\times25\times7}\)         ( 4^3 = 8^2 ; 5^4 = 25^2 )

\(=\frac{1}{25\times7}=\frac{1}{175}\)

\(a.\frac{-9}{-12}=\frac{-9:3}{-12:3}=\frac{-3}{-4}.\)

\(\frac{-18}{-24}=\frac{-18:6}{-24:6}=\frac{-3}{-4}\)

\(\frac{-35}{-70}=\frac{-35:35}{-70:35}=\frac{-1}{-2}\)

\(\frac{-9}{-27}=\frac{-9:9}{-27:9}=\frac{-1}{-3}\)

a) \(\frac{-9}{12}=\frac{-9\div3}{12\div3}=\frac{-3}{4}\)

\(\frac{-18}{-24}=\frac{-18\div\left(-6\right)}{-24\div\left(-6\right)}=\frac{3}{4}\)

\(\frac{-35}{70}=\frac{-35\div35}{70\div35}=\frac{-1}{2}\)

\(\frac{-9}{27}=\frac{-9\div9}{27\div9}=\frac{-1}{3}\)

b) \(\frac{1313}{4242}=\frac{1313\div101}{4242\div101}=\frac{13}{42}\)

\(\frac{-353535}{-424242}=\frac{-353535\div\left(-70707\right)}{-424242\div\left(-70707\right)}=\frac{5}{6}\)

c)\(\frac{2^3\times4^3\times5^4}{8^2\times25^3\times7}\)= \(\frac{2^3\times4^3\times5^4}{\left(2^3\right)^2\times\left(5^2\right)^3\times7}\)= \(\frac{2^3\times4^3\times5^4}{2^6\times5^6\times7}\)= \(\frac{2^3\times4^3\times5^4}{2^3\times2^3\times5^2\times5^4\times7}\)= \(\frac{2^3\times2^3}{2^3\times5^2\times7}\)= \(\frac{8}{25\times7}\)= \(\frac{8}{175}\)

a,\(\frac{2015.2016+2015-1}{2014+2015.2016}=\frac{2015.2016+2014}{2014+2015.2016}=1\)\(1\)

b,\(=1-\frac{1}{5}+\frac{1}{5}...-\frac{1}{2011}+\frac{1}{2011}-\frac{1}{2015}=1-\frac{1}{2015}=\frac{2014}{2015}\)

c,\(=\frac{12}{35}+\frac{12}{35}+\frac{12}{35}+\frac{12}{35}=\frac{12}{35}.4=\frac{48}{35}\)

48/35 nha

b>=1-1/5+1/5-1/9+...+1/2011-1/2015

 =1-1/2015

=2014/2015

c>=12/35+12/35+12/35+12/35

=12/35x4

=48/35