\(\frac{x-12}{3}=\frac{x+1}{4}\)

=>(x-12).4=(x+1)*3

    4x-48=3x+3

    4x-3x=48+3

    x=51

(x-12)/3=(x+1)/4

(x-12)*4=(x+1)*3

x*4-12*4=x*3+1*3

4x-48=3x+3

4x-3x=3+48

x=51

\(A=\frac{1}{4}+\frac{1}{9}+\frac{1}{16}+...+\frac{1}{100}\)

\(A=\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{10^2}\)

\(A< \frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{9.10}\)

\(A< 1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{9}-\frac{1}{10}\)

\(A< 1-\frac{1}{10}=\frac{9}{10}\)

\(=>A>\frac{65}{132}\)

Ta có: \(A=\frac{1}{2^2}+\frac{1}{4^2}+\frac{1}{6^2}+\frac{1}{8^2}+\frac{1}{10^2}+\frac{1}{12^2}+\frac{1}{14^2}\)

              \(=\frac{1}{2^2}\left(1+\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+\frac{1}{5^2}+\frac{1}{6^2}+\frac{1}{7^2}\right)\)  

            \(< \frac{1}{2^2}\left(1+\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}\right)\)  

            \(=\frac{1}{2^2}\left(1+1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}\right)\)

             \(=\frac{1}{2^2}\left(2-\frac{1}{7}\right)=\frac{1}{2}-\frac{1}{28}< \frac{1}{2}\)

 Vậy   \(A< \frac{1}{2}\).

a)\(\frac{3}{5}+\frac{4}{7}=\frac{21}{35}+\frac{20}{35}=\frac{41}{35}\)

b)\(\frac{2}{3}-\frac{3}{9}=\frac{2}{3}-\frac{1}{3}=\frac{1}{3}\)Hoặc \(\frac{2}{3}-\frac{3}{9}=\frac{6}{9}-\frac{3}{9}=\frac{3}{9}=\frac{1}{3}\)

c)\(\frac{2}{5}\)x\(\frac{8}{11}=\frac{16}{55}\)

d)\(\frac{3}{7}:\frac{6}{14}=\frac{3}{7}\)x\(\frac{14}{6}=\)\(\frac{3x7x2}{7x3x2}\)\(=\)\(1\)

e)\(\frac{3}{8}+\frac{6}{15}:\frac{3}{5}=\frac{3}{8}+\frac{6}{15}\)x\(\frac{5}{3}=\frac{3}{8}+\)\(\frac{2}{3}\)\(=\frac{9}{24}+\frac{16}{24}=\frac{25}{24}\)

Giải cực kì đầy đủ

mình không biết nữa bằng bao nhiêu ấy nhỉ .......? .......? Sory ^.^

1/3 + 13/15 + 33/35 + 61/63 + 97/99

= 45/11 ( mình không tiện giải, để khi khác giải sau)

Chúc bạn may mắn!

   45^12 : 25^6 : 3^2

= (45^6)^2 : (25^3)^2 : 3^2

= (8303765625 : 15625 : 3)^2

= 177147^2

a) \(\frac{3}{8}:\frac{9}{10}=\frac{3}{8}\cdot\frac{10}{9}=\frac{30}{72}=\frac{5}{12}\)

b) \(\frac{4}{9}:\frac{12}{8}=\frac{4}{9}\cdot\frac{8}{12}=\frac{32}{108}=\frac{8}{27}\)

Xin lỗi, bài này mk ko biết tính bằng cách thuận tiện, chỉ biết làm thế này thôi!!

a) 5/12

b) 8/27