\(a)\frac{1}{5}\times\frac{1}{2}:\frac{1}{3}=\frac{1}{5}\times\frac{1}{2}\times\frac{3}{1}=\frac{1\times1\times3}{5\times2\times1}=\frac{1\times3}{5\times2}=\frac{3}{10}\)

\(b)\frac{2}{9}:\frac{2}{3}\times\frac{1}{2}=\frac{2}{9}\times\frac{3}{2}\times\frac{1}{2}=\frac{2\times3\times1}{9\times2\times2}=\frac{1\times1\times1}{3\times1\times2}=\frac{1}{6}\)

\(c)\frac{1}{2}\times\frac{1}{3}+\frac{1}{4}=\frac{1}{6}+\frac{1}{4}=\frac{2}{12}+\frac{3}{12}=\frac{2+3}{12}=\frac{5}{12}\)

d, Tương tự như câu c

P/S : Bất phương trình????

\(\frac{1}{5}\times\frac{1}{2}:\frac{1}{3}\)

\(=\frac{1}{10}\times\frac{3}{1}\)

\(=\frac{3}{10}\)

\(\frac{2}{9}:\frac{2}{3}\times\frac{1}{2}\)

\(=\frac{2}{9}\times\frac{3}{2}\times\frac{1}{2}\)

\(=\frac{1}{3}\times\frac{1}{1}\times\frac{1}{2}\)

\(=\frac{1}{3}\times\frac{1}{2}\)

\(=\frac{1}{6}\)

=1/2 + 2/7 - 10/11 + -1/3 + 3/5 - 8/21 + 7/10 = ( 1/2 + 3/5 + 7/10 ) + ( 2/7 + -1/3 - 8/21 ) - 10/11 = 9/5 + -3/7 - 10/11 = 178/385

Tính 

a ) 5/2 x 1/3 + 1/4

= 5/5+1/4

=13/12

b)5/2 +  1/3 x 1/4

= 5/2 + 1/12

= 31/12

c ) 5/2 -1/3 :1/4

= 5/2  - 4/3

= 7/6

tk mk nha ( nếu đúng )

hihi mơn nha !!!!!!!!!!

a. = (5/2x2/3) +1/4

    = 5/3+1/4= 23/12

b. = 5/2+( 1/3x1/4)

    = 5/2+1/12

    =31/12

c. =5/2-( 1/3:1/4)

    = 5/2-4/3

    = 7/6

A, 5/2×1/3+1/4

  =5/6+1/4

  =13/12

B, 5/2+1/3×1/4

  =5/2+1/12

  =5/2—1/3:1/4

  =5/2—4/3

  =7/6

k mk nha

=

C, 5/2

Ta có: \(a=\left(x+y\right)\left(x^2-xy+y^2\right)-2y^3\)

\(=x^3+y^3-2y^3\)

\(=x^3-y^3\)

\(=\left(\dfrac{2}{3}\right)^3-\left(\dfrac{1}{3}\right)^3=\dfrac{8}{27}-\dfrac{1}{27}=\dfrac{7}{27}\)

= 1 là đúng

Bạn có thể cho mình biết cách giải được không vậy bạn.

\(\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+...+\frac{1}{\left(2x+1\right).\left(2x+3\right)}=\frac{15}{93}\)

\(2.\left(\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+...+\frac{1}{\left(2x+1\right).\left(2x+3\right)}\right)=2.\frac{15}{93}\)

\(\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+...+\frac{2}{\left(2x+1\right).\left(2x+3\right)}=\frac{30}{93}\)

\(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{2x+1}-\frac{1}{2x+3}=\frac{10}{31}\)

\(\frac{1}{3}-\frac{1}{2x+3}=\frac{10}{31}\)

\(\frac{1}{2x+3}=\frac{1}{3}-\frac{10}{31}\)

\(\frac{1}{2x+3}=\frac{1}{93}\)

=> 2x + 3 = 93

=> 2x = 93 - 3

=> 2x = 90

=> x = 90 : 2

=> x = 45

Vậy x = 45

sai rồi

Đặt \(A=\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{\left(2x+1\right).\left(2x+3\right)}\)

\(2A=\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{\left(2x+1\right).\left(2x+3\right)}\)

\(2A=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{2x+1}-\frac{1}{2x+3}\)

\(2A=\frac{1}{3}-\frac{1}{2x+3}\)

\(A=\frac{2x}{3\left(2x+3\right)}:2\)

\(\Rightarrow\frac{2x}{3\left(2x+3\right)}:2=\frac{15}{93}\)

\(\frac{2x}{3\left(2x+3\right)}=\frac{15}{93}.2=\frac{30}{93}=\frac{10}{31}\)

\(\frac{2x}{6x+9}=\frac{10}{31}\)

\(\Rightarrow2x.31=10.\left(6x+9\right)\)

\(\Rightarrow62x=60x+90\)

\(62x-60x=90\)

\(2x=90\)

\(x=45\)

Vậy x = 45

Ủng hộ mk nha !!! ^_^

Mẫu số=19/1+18/2+17/3+...+2/18+1/19

=(1+1+1+...+1)+(18/2+17/3+...+2/18+1/19)

(19 số 1)                      (18 phân số)

=(1+18/2)+(1+17/3)+...+(1+2/18)+(1+1/19)+1

=20/2+20/3+...+20/18+20/19+20/20

=20.(1/2+1/3+...+1/18+1/19+1/20)

Phân số trên=1/20

\(\Rightarrow A=\frac{1}{\frac{\left(2+1\right).2}{2}}+\frac{1}{\frac{\left(3+1\right).3}{2}}+\frac{1}{\frac{\left(4+1\right).4}{2}}+...+\frac{1}{\frac{\left(99+1\right).99}{2}}+\frac{1}{50}\)

\(=\frac{2}{\left(2+1\right).2}+\frac{2}{\left(3+1\right).3}+\frac{2}{\left(4+1\right).4}+...+\frac{2}{\left(99+1\right).99}+\frac{1}{50}\)

\(=2.\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{99.100}\right)+\frac{1}{50}\)

\(=2.\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{99}-\frac{1}{100}\right)+\frac{1}{50}\)

\(=2.\left(\frac{1}{2}-\frac{1}{100}\right)+\frac{1}{50}\)

\(=2.\frac{49}{100}+\frac{1}{50}\)

\(=\frac{49}{50}+\frac{1}{50}=\frac{50}{50}=1\)

Vậy A=1.

Cái này có trong violympic vòng 10..bạn nhớ ôn cho kĩ nếu như bạn thi violympic!

=1 đó bạn , dễ mà , tick nhé