\(a,\frac{42}{25}:\frac{y}{5}=\frac{6}{5}\)

\(\frac{y}{5}=\frac{42}{25}:\frac{6}{5}\)

\(\frac{y}{5}=\frac{42}{25}\times\frac{5}{6}\)

\(\frac{y}{5}=\frac{7}{5}\)

\(\Leftrightarrow5y=7.5\)

\(5y=35\)

\(y=7\)

\(b,\frac{24}{y}:\frac{8}{3}=\frac{3}{5}\)

\(\frac{24}{y}=\frac{3}{5}\times\frac{8}{3}\)

\(\frac{24}{y}=\frac{8}{5}\)

\(\Leftrightarrow8y=24.5\)

\(8y=120\)

\(y=15\)

\(\frac{5}{6}y=\frac{3}{2}\)

\(y=\frac{3}{2}:\frac{5}{6}\)

\(y=\frac{3}{2}\times\frac{6}{5}\)

\(y=\frac{9}{5}\)

bài 1

A)37/60

B)13/45

C)1/4

bài 2

a)42/25:y/5=5/6

y=10,08

b)27/y:9/4=3/7

y=28

a) \(\dfrac{5}{y}=\dfrac{1}{2}\)

\(y=\dfrac{5\times2}{1}=10\)

b) \(\dfrac{42}{25}:\dfrac{y}{5}=\dfrac{6}{5}\)

\(\dfrac{y}{5}=\dfrac{42}{25}:\dfrac{6}{5}\)

\(\dfrac{y}{5}=\dfrac{7}{5}\)

\(y=7\)

\(\dfrac{5}{y}=\dfrac{1}{2}\\ =>y=5.2:1=10\)

\(\dfrac{42}{25}:\dfrac{y}{5}=\dfrac{6}{5}\\ =>\dfrac{y}{5}=\dfrac{42}{25}:\dfrac{6}{5}=\dfrac{42}{25}.\dfrac{5}{6}=\dfrac{7}{5}\\ =>y=\dfrac{7}{5}.5=7\)

a) \(\dfrac{5}{y}=\dfrac{1}{2}\)

\(\Rightarrow y=5\cdot2:1=10\)

b) \(\dfrac{42}{25}:\dfrac{y}{5}=\dfrac{6}{5}\)

\(\dfrac{y}{5}=\dfrac{42}{25}:\dfrac{6}{5}=\dfrac{7}{5}\)

\(\dfrac{y}{5}=\dfrac{7}{5}\)

\(\Rightarrow y=7\)

C

\(a,\dfrac{x}{5}=\dfrac{-18}{10}\\ \Rightarrow x=-\dfrac{18}{10}.5\\ \Rightarrow x=-9\\ b,\dfrac{6}{x-1}=\dfrac{-3}{7}\\ \Rightarrow6.7=-3\left(x-1\right)\\ \Rightarrow42=-3x+3\\ \Rightarrow42+3x-3=0\\ \Rightarrow3x+39=0\\ \Rightarrow3x=-39\\ \Rightarrow x=-13\\ c,\dfrac{y-3}{12}=\dfrac{3}{y-3}\\ \Rightarrow\left(y-3\right)^2=36\\ \Rightarrow\left[{}\begin{matrix}y-2=6\\y-2=-6\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}y=8\\y=-4\end{matrix}\right.\)

\(d,\dfrac{x}{25}=\dfrac{-5}{x^2}\\ \Rightarrow x^3=-125\\ \Rightarrow x^3=\left(-5\right)^3\\ \Rightarrow x=-5\)

1a) \(\frac{x-3}{x+7}=\frac{-5}{-6}\)

=> \(\frac{x-3}{x+7}=\frac{5}{6}\)

=> (x - 3).6 = 5.(x + 7)

=> 6x - 18 = 5x + 35

=> 6x - 5x = 35 + 18

=> x = 53

b) \(\frac{x-7}{x+3}=\frac{4}{3}\)

=> (x - 7). 3 = (x + 3). 4

=> 3x - 21 = 4x + 12

=> 3x - 4x = 12 + 21

=> -x = 33

=> x = -33

c) \(\frac{x-10}{6}=-\frac{5}{18}\)

=> (x - 10) . 18 = -5 . 6

=> 18x - 180 = -30

=> 18x = -30 + 180

=> 18x = 150

=> x = 150 : 18 = 25/3

d) \(\frac{x-2}{4}=\frac{25}{x-2}\)

=> (x - 2)(x - 2) = 25 . 4

=> (x - 2)² = 100

=> (x - 2)² = 10²

=> \(\orbr{\begin{cases}x-2=10\\x-2=-10\end{cases}}\)

=> \(\orbr{\begin{cases}x=12\\x=-8\end{cases}}\)

e) \(\frac{7}{x}=\frac{x}{28}\)

=> 7 . 28 = x . x

=> 196 = x²

=> x² = 14²

=> \(\orbr{\begin{cases}x=14\\x=-14\end{cases}}\)

f) \(\frac{40+x}{77-x}=\frac{6}{7}\)

=> (40 + x) . 7 = (77 - x).6

=> 280 + 7x = 462 - 6x

=> 280 - 462 = -6x + 7x

=> -182 = x

=> x = -182

36367 l'290209 92021

24/y=3/5*8/3

24/y=8/5

24:y=8/5

y=24;8/5

y=15

b,42/25:y/5=6/7

y/5=42/25:6/7

y/5=49/25

y:5=49/25

y=49/25*5

y=49/5=9,8

\(\frac{24}{y}:\frac{8}{3}=\frac{3}{5}\)

\(\Rightarrow\frac{24}{y}=\frac{3}{5}\times\frac{8}{3}\)

\(\Rightarrow\frac{24}{y}=\frac{8}{5}\)

\(\Rightarrow y=\frac{8}{5}\times24=\frac{192}{5}\)

b , \(\frac{42}{25}:\frac{y}{5}=\frac{6}{7}\)

\(\Rightarrow\frac{y}{5}=\frac{6}{7}\times\frac{42}{25}=\frac{36}{25}\)

\(\Rightarrow y=\frac{36}{25}\times5=\frac{36}{5}\)

\(\frac{24}{y}:\frac{8}{3}=\frac{3}{5}\)                \(\frac{42}{25}:\frac{y}{5}=\frac{6}{7}\)

\(\frac{24}{y}=\frac{3}{5}\cdot\frac{8}{3}\)                      \(\frac{y}{5}=\frac{42}{25}:\frac{6}{7}\)

\(\frac{24}{y}=\frac{8}{5}\)                                \(\frac{y}{5}=\frac{42}{25}\cdot\frac{7}{6}\)

\(\Rightarrow8y=24\cdot5\)                         \(\frac{y}{5}=\frac{49}{25}\)

\(8y=120\)                                 \(\Rightarrow25y=5\cdot49\)

\(y=15\)                                            \(25y=245\)

                                                                \(y=\frac{49}{5}\) 

\(y+y.\frac{1}{3}.\frac{9}{2}+y.\frac{7}{2}=25\)

\(y+y.6+y.\frac{7}{2}=25\)

\(y.\left(1+6+\frac{7}{2}\right)=25\)

\(y.\frac{21}{2}=25\)

\(y=25:\frac{21}{2}\)

\(y=25.\frac{2}{21}\)

\(y=\frac{50}{21}\)

\(y.5+y.3+y+y=50\)

\(y.\left(5+3+1+1\right)=50\)

\(y.10=50\)

\(y=5\)

\(y:4+y:3+y=\frac{5}{6}\)

\(y.\frac{1}{4}+y.\frac{1}{3}+y=\frac{5}{6}\)

\(y.\left(\frac{1}{4}+\frac{1}{3}+1\right)=\frac{5}{6}\)

\(y.\frac{19}{12}=\frac{5}{6}\)

\(y=\frac{5}{6}:\frac{19}{12}\)

\(y=\frac{5}{6}.\frac{12}{19}\)

\(y=\frac{10}{19}\)

d) Áp dụng tính chất dãy tỉ số bằng nhau ta có :

\(\frac{x}{7}=\frac{y}{13}=\frac{x+y}{7+13}=\frac{40}{20}=2\)

\(\frac{x}{7}=2\Rightarrow x=14\)

\(\frac{y}{13}=2\Rightarrow y=26\)

Vậy x=14 và y=26