a, 7/5 : x + 3/2 = 16/3

7/5 : x = 16/3 - 3/2

7/5 : x = 23/6

x = 7/5 : 23/6

x = 42/115

b, x : 1/5 + 1/7 = 3/5 . 18/21

x : 1/5 + 1/7 = 18/35

x : 1/5 = 18/35 - 1/7

x : 1/5 = 13/35

x = 13/35 . 1/5

x = 13/175

c, x - 1 và 1/3 : 2 = 5/7

x - 4/3 : 2 = 5/7

x - 4/3 = 5/7 . 2

x - 4/3 = 10/7

x = 10/7 + 4/3

x = 58/21

d, x + 2 và 3/5 . 1/6 = 35/36

x + 13/5 . 1/6 = 35/36

x + 13/5 = 35/36 : 1/6

x + 13/5 = 35/6

x = 35/6 - 13/5

x = 97/30

e, ( x + 3/2 ) : 2 = 7/10 + 1/5

( x + 3/2 ) : 2 = 9/10

x + 3/2 = 9/10 . 2

x + 3/2 = 9/5

x = 9/5 - 3/2

x = 3/10

\(\left(a\right)\frac{34-x}{30}=\frac{5}{6}\)

\(\frac{34-x}{30}=\frac{25}{30}\)

34 - x = 25

x = 34 - 25 = 9

\(\left(b\right)\frac{x+13}{34}=\frac{12}{17}\)

\(\frac{x+13}{34}=\frac{24}{34}\)

x + 13 = 24

x = 24 - 13 = 11

\(\left(c\right)\left(x+\frac{1}{3}\right)+\left(x+\frac{1}{9}\right)+\left(x+\frac{1}{27}\right)+\left(x+\frac{1}{81}\right)=\frac{56}{81}\)

\(4x+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}=\frac{56}{81}\)

Đặt \(A=\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}\)

Ta có : \(3A=1+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}\)

\(3A-A=1+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}-\frac{1}{3}-\frac{1}{9}-\frac{1}{27}-\frac{1}{81}\)

\(2A=1-\frac{1}{81}=\frac{80}{81}\)

\(A=\frac{80}{81}\div2=\frac{40}{81}\)

\(\Rightarrow4x+\frac{40}{81}=\frac{56}{81}\)

\(4x=\frac{56}{81}-\frac{40}{81}\)

\(4x=\frac{16}{81}\)

\(x=\frac{16}{81}\div4=\frac{4}{81}\)

a, \(\frac{34-x}{30}=\frac{5}{6}\Leftrightarrow\frac{34-x}{30}=\frac{25}{30}\)

\(\Leftrightarrow34-x=25\Leftrightarrow x=9\)

b, \(\frac{x+13}{34}=\frac{12}{17}\Leftrightarrow\frac{x+13}{34}=\frac{24}{34}\)

\(\Leftrightarrow x+13=24\Leftrightarrow x=11\)

a)\(\frac{x}{17}=\frac{60}{204}=\frac{5}{17}\Rightarrow x=5\)

b)\(\frac{6+x}{33}=\frac{7}{11}\Rightarrow11\left(6+x\right)=7.33\Rightarrow11.6+11x=231\Rightarrow66+11x=231\)

\(\Rightarrow11x=231-66\Rightarrow11x=165\Rightarrow x=\frac{165}{11}=15\)

c)\(\frac{12+x}{43-x}=\frac{2}{3}\Rightarrow2\left(43-x\right)=3\left(12+x\right)\Rightarrow2.43-2x=3.12+3x\)

\(86-2x=36+3x\Rightarrow86-36=3x+2x\Rightarrow50=5x\Rightarrow x=\frac{50}{5}=10\)

a)\(=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}.\frac{4}{5}......\frac{99}{100}\)

\(=\frac{1.2.3.4.....99}{2.3.4.5.6.....100}\)

\(=\frac{1}{100}\)

b) Tương tự như câu a

Ra kết quả phần b là \(\frac{101}{2}\) đúng hông?

a) X = 15

b) X = 4

c ) X= 23

d) X= 11

( Chỉ là ý kiến riêng thôi nhé, nhận gạch đá )

a) \(\frac{6+x}{33}=\frac{7}{11}\)

=> (6 + x). 11 = 33.7

=> 66 + 11x = 231

=> 11x = 231 - 66

=> 11x = 165

=> x = 165 : 11

=> x = 15

b) 15/26 + x/13 = 46/52

=> x/13 = 23/26 - 15/26

=> x/13 = 4/13

=> x = 4

c) 121/27 x 54/11 < x < 100/21 : 25/126

=> 22 < x < 24

=> x = 23 (vì x là số tự nhiên)

d) 1 < 11/x < 12

=> 11/x \(\in\){2; 3; 4 ; ...; 11}

=> x \(\in\) {11/2; 11/3; ...; 1}

Vì x là số tự nhiên => x = 1

a, 3/4 + 1/4.x=2

    1/4.x        = 2-3/4

     1/4.x      =5/4

     x           = 5/4:1/4

     x           = 5

b, x-2/3.9/4=2,5-1/2

    x-2/3.9/4=2

    x-2/3     =2:9/4

    x-2/3   =8/9

     x        = 8/9+2/3

     x         = 14/9

a) \(\frac{3}{5}+\frac{6}{11}+\frac{7}{13}+\frac{5}{11}+\frac{2}{5}+\frac{19}{13}=\left(\frac{3}{5}+\frac{2}{5}\right)+\left(\frac{6}{11}+\frac{5}{11}\right)+\left(\frac{7}{13}+\frac{19}{13}\right)=1+1+2=4\)

b) \(\frac{6}{5}\times\frac{3}{8}+\frac{5}{8}\times\frac{6}{5}-\frac{4}{5}=\frac{6}{5}\times\left(\frac{3}{8}+\frac{5}{8}\right)-\frac{4}{5}=\frac{6}{5}-\frac{4}{5}=\frac{2}{5}\)

c) \(\frac{4\times5\times6\times7\times8}{8\times10\times12\times14\times16}=\frac{1}{2\times2\times2\times2\times2}=\frac{1}{32}\)

a, \(\frac{3}{5}+\frac{6}{11}+\frac{7}{13}+\frac{6}{11}+\frac{2}{5}+\frac{19}{13}\)

\(=\left(\frac{3}{5}+\frac{2}{5}\right)+\left(\frac{7}{13}+\frac{19}{13}\right)+\left(\frac{6}{11}+\frac{6}{11}\right)\)

\(=1+2+\frac{12}{11}\)

\(=3+\frac{12}{11}\)

\(=\frac{45}{11}\)