a)13/17 < 15/19

a) 2/3 x X + 3/4 = 3

          2/3 x X    = 3 - 3/4

          2/3 x X    = 9/4

                   X    = 9/4 : 2/3

                   X    = 27/8

a. Ta có : \(\frac{13}{17}=\frac{247}{323};\frac{15}{19}=\frac{255}{323}\)

Vì 255 > 247 nên 247/323 < 255/323 

Hay \(\frac{13}{17}< \frac{15}{19}\)

b. \(\frac{2}{3}\times x+\frac{3}{4}=3\)

\(\frac{2}{3}\times x=3-\frac{3}{4}\)

\(\frac{2}{3}\times x=\frac{9}{4}\)

\(x=\frac{9}{4}:\frac{2}{3}\)

\(x=\frac{27}{8}\)

c. \(720:\left[41-\left(2\times x-5\right)\right]=120\)

\(\left[41-\left(2\times x-5\right)\right]=720:120\)

\(41-\left(2\times x-5\right)=6\)

\(2\times x-5=35\)

\(2\times x=40\)

\(x=20\)

a)\(\frac{13}{17}>\frac{15}{19}\)

b)\(720\div[41-(2x\times5)]=120\)                                 c)\(\frac{2}{3}\times x+\frac{3}{4}=3\)

   \(41-(2x\times5)=270\div120\)                                          \(\frac{2}{3}\times x=3-\frac{3}{4}\)

    \(41-(2x-5)=6\)                                                               \(\frac{2}{3}\times x=\frac{9}{4}\)

     \(2x-5=41-6\)                                                                     \(x=\frac{9}{4}\div\frac{2}{3}\)

     \(2x-5=35\)                                                                                \(x=\frac{9}{4}\times\frac{3}{2}\)

     \(2x=35+5\)                                                                                \(x=\frac{27}{8}\)

      \(2x=40\)

      \(x=40\div2\)

      \(x=20\)

Ta có:\(\frac{17}{52}< \frac{17}{51}hay\frac{17}{52}< \frac{1}{3}\)(1)

\(\frac{41}{120}>\frac{40}{120}hay\frac{41}{120}>\frac{1}{3}\)(2)

Từ (1)và(2) =>\(\frac{17}{52}< \frac{1}{3}< \frac{41}{120}\)

Hay \(\frac{17}{52}< \frac{41}{120}\)

Vậy không quy đồng mẫu số và tử số ta được:\(\frac{17}{52}< \frac{41}{120}\)

Học giỏi^^

lên mạng mà xem

Thanks ban

\(\frac{16}{51}< \frac{31}{90}\)

16*3=48<51<31*3=93>90

=>16/51 < 31/90

Ta có\(\frac{16}{51}< \frac{17}{51}=\frac{1}{3};\frac{31}{90}>\frac{30}{90}=\frac{1}{3}\) 

\(\Rightarrow\frac{16}{51}< \frac{1}{3}< \frac{31}{90}\Rightarrow\frac{16}{51}< \frac{31}{90}\)

31/90<32/80

van de la chung minh the nao ban ah

khong can nua da giai dc roi

\(\left\{{}\begin{matrix}a=32^{81}\\b=31^{90}\end{matrix}\right.\)

\(\dfrac{a}{b}=\dfrac{2^{5.3^4}}{31^{2.3^2.5}}=\left(\dfrac{2^{3^2}}{31^2}\right)^{^{5.3^2}}\)

\(\dfrac{2^{10}}{2.31^2}< \dfrac{1024}{2.30^2}=\dfrac{1024}{1800}< 1\Rightarrow\dfrac{a}{b}< 1\Rightarrow a< b\)