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Ta có \(\frac{x-3}{y-2}=\frac{3}{2}\)

Nên 2 ( x - 3 ) = 3 ( y - 2 )

Do đó 2x - 6 = 3y - 6 nên 2x = 3y

Suy ra 2x - 2y = y hay 2 ( x - y ) = y

Mà x - y = 4 nên 2.4 = y

Suy ra y = 8

\(x=\frac{3y}{2}=\frac{3.8}{2}=12\)

Vây x = 12 ; y = 8

\(\frac{x-3}{y-2}=\frac{3}{2}\)

=> \(\left(x-3\right).2=3\left(y-2\right)\)

=> \(2x-6=3y-6\)

=> \(2x=3y\)

Khi đó ,ta có: x - y = 4

=> 2(x - y) = 8

=> 2x - 2y = 8

=> 3y - 2y = 8

=> y = 8 

     => x = 4 + 8 = 12

Vậy x = 12 và y = 8

\(\frac{x-3}{y-2}=\frac{3}{2}\)

=> 2. ( x - 3 ) = 3.( y - 2 )

=> 2x - 6 = 3y - 6

=> 2x  = 3y

=> \(\frac{x}{3}=\frac{y}{2}\)

Áp dụng tính chất dãy tỉ số bằng nhau.

=> \(\frac{x}{3}=\frac{y}{2}=\frac{x-y}{3-2}\)\(=\frac{4}{1}=4\)

=> \(\hept{\begin{cases}x=3.4=12\\y=2.4=8\end{cases}}\)

Vậy x = 8, y = 12

ta có:\(\frac{x-3}{y-2}=\frac{3}{2}\)

\(\Rightarrow\frac{x-3}{3}=\frac{y-2}{2}=\frac{x-3-y+2}{3-2}=\frac{\left(x-y\right)-\left(3-2\right)}{1}=\frac{4-1}{1}=3\)

=> x-3/3 = 3 => x-3 = 9 => x = 12

y-2/2 = 3 => y-2 = 6=> y = 8

ta có: x-y = 4 => x = 4 + y

Lại có: \(\frac{x-3}{y-2}=\frac{3}{2}\)

=> (x-3).2 = (y-2).3

2x - 6 = 3y - 6

2x -3y = -6+6

=> 2.(4+y) - 3y = 0

8 + 2y - 3y = 0

8 - y = 0

y = 8

=> \(\frac{x-3}{8-2}=\frac{x-3}{6}=\frac{3}{2}\)

=> x-3 = 9

x = 12

Ta có: \(\frac{x-3}{y-2}=\frac{3}{2}\)

=> (x - 3) . 2 = (y - 2) . 3

=> 2x - 6 = 3y - 6

=> 2x = 3y

=> x = 3/2y

Khi đó, ta có: x - y = 4

hay 3/2y - y = 4

=> 1/2y = 4

=> y = 4 : 1/2

=> y = 8

=> x = 4 + 8 = 12

Vậy x = 12 và y = 8

Theo đề:\(\frac{x-3}{y-2}=\frac{3}{2}\Rightarrow2\left(x-3\right)=3\left(y-2\right)\)

\(\Rightarrow2x-6=3y-6\)

\(\Rightarrow2y-3y=-6+6\)

Vì\(x-y=4\Rightarrow x=4+y\)

\(\Rightarrow2\left(y+4\right)-3y=0\)

\(\Rightarrow2y+8-3y=0\)

\(\Rightarrow-y=-8\Rightarrow y=8\)

\(\Rightarrow x=y+4=8+4=12\)

Vậy y=8;x=12

\(x-y=4\Rightarrow x=4+y\)

\(\frac{x-3}{y-2}=\frac{3}{2}\Rightarrow\frac{4+y-3}{y-2}=\frac{3}{2}\)

\(\Rightarrow\frac{y+1}{y-2}=\frac{3}{2}\)

\(\Rightarrow\left(y+1\right)\cdot2=\left(y-2\right)\cdot3\)

\(\Rightarrow2y+2=3y-6\)

\(\Rightarrow3y-2y=6+2\)

\(\Rightarrow y=8\)

Thay y vào x - y = 4. Ta có:

\(x-y=4\Rightarrow x-8=4\)

\(\Rightarrow x=8+4=12\)

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

\(\Rightarrow\frac{x}{3}=\frac{y}{2}=\frac{x-y}{3-2}=\frac{4}{1}=4\)

=>x=12;y=8

\(\frac{x}{4}-\frac{2}{y}=\frac{3}{2}\)=) \(\frac{2}{y}=\frac{x}{4}-\frac{3}{2}=\frac{x-6}{4}\)
=) \(y\left(x-6\right)=2.4=8\)
=) \(y,x-6\inƯ\left(8\right)=\left\{-1,1,-2,2,-4,4,-8,8\right\}\)
Rồi lập bảng tìm x,y

\(\frac{x}{4}-\frac{2}{y}=\frac{3}{2} \left(x,y\in Z ; y\ne0\right)\)

\(\Leftrightarrow xy-8=6y\Leftrightarrow y\left(x-6\right)=8\)

Giải các trường hợp dễ dàng.... Bạn tự làm tiếp nhé

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

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

\(\frac{2}{y}=\frac{x-6}{4}\)

\(\Rightarrow\)y(x-6)=8

\(y\inƯ\left(8\right)\\ x-6\inƯ\left(8\right)\)

mà Ư(8)={1;-1;2;-2;4;-4;8;-8}

Ta lập bảng

Vậy (x,y)={(8,7);(-8,5);(4,8);(-4,4);(2,10);(-2,2);(1,14);(-1,-2)}

\(\frac{x-2}{27}+\frac{x-3}{26}+\frac{x-4}{25}+\frac{x-5}{24}+\frac{x-44}{5}=1\)

\(\Leftrightarrow\left(\frac{x-2}{27}-1\right)+\left(\frac{x-3}{26}-1\right)+\left(\frac{x-4}{25}-1\right)+\left(\frac{x-5}{24}-1\right)\)\(+\left(\frac{x-44}{5}+3\right)=1-1\)

\(\Leftrightarrow\frac{x-29}{27}+\frac{x-29}{26}+\frac{x-29}{25}+\frac{x-29}{24}\)\(+\frac{x-29}{5}=0\)

\(\Leftrightarrow\left(x-29\right)\left(\frac{1}{27}+\frac{1}{26}+\frac{1}{25}+\frac{1}{24}+\frac{1}{5}\right)=0\)

Mà \(\frac{1}{27}+\frac{1}{26}+\frac{1}{25}+\frac{1}{24}+\frac{1}{5}\ne0\)

=> x - 29 = 0

=> x = 29.

\(\frac{x-3}{y-2}=\frac{3}{2}\Rightarrow2x-6=3y-6\)

\(\Rightarrow2x-6+6=3y\)

\(\Rightarrow2x=3y\Rightarrow\frac{x}{3}=\frac{y}{2}\)

Theo t)c của dãy tỉ số bằng nhau : 

\(\Rightarrow\frac{x}{3}=\frac{y}{2}=\frac{x-y}{3-2}=\frac{4}{1}=4\)

\(\Rightarrow x=4.3=12;y=4.2=8\)

1, ta co \(\frac{x}{5}=\frac{y}{6}=\frac{x}{20}=\frac{y}{24}\)

\(\frac{y}{8}=\frac{z}{7}=\frac{y}{24}=\frac{z}{21}\)

=>\(\frac{x}{20}=\frac{y}{24}=\frac{z}{21}=\frac{x+y-z}{20+24-21}=\frac{69}{23}=3\)

=>\(x=3\cdot20=60\)

    \(y=3\cdot24=72\)

    \(z=3\cdot21=63\)

3. ta co \(\frac{x}{15}=\frac{y}{7}=\frac{z}{3}=\frac{t}{1}=\frac{x+y-z+t}{15-7+3-1}=\frac{10}{10}=1\)

=> \(x=1\cdot15=15\)

     \(y=1\cdot7=7\)

     \(z=1\cdot3=3\)

     \(t=1\cdot1=1\)

Áp dụng tính chất dãy tỉ số bằng nhau

\(\frac{x}{5}=\frac{y}{7}=\frac{z}{9}=\frac{x-y+z}{5-7+9}=\frac{315}{7}=45\)

  suy ra:   x/5 = 45   =>  x  =  225

               y/7 = 45  =>  y  =  315

               z/9 = 45  =>  z  =  405