bài 1

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

\(\Rightarrow\left(3x-y\right).4=\left(x+y\right)3\)

\(\Rightarrow12x-4y=3x+3y\)

\(\Rightarrow9x=7y\)

\(\Rightarrow\frac{x}{y}=\frac{7}{9}\)

Vậy \(\frac{x}{y}=\frac{7}{9}\)

\(\frac{6}{11}x=\frac{9}{2}y=\frac{18}{5}z\Rightarrow\frac{6x}{11.18}=\frac{9y}{2.18}=\frac{18z}{5.18}\)

\(\Rightarrow\frac{-x}{-33}=\frac{y}{4}=\frac{z}{5}=\frac{-x+y+z}{-33+4+5}=\frac{-120}{-24}=5\)

\(\Rightarrow x=165;y=20;z=25\)

ta có : 1/y = x/4 - 1/2 = ( x+2)/4 <=> y = 4/(x - 2)

Để x, y nguyên nên ta có : x-2 ϵ Ư(4) = { -1 , 1 ,-2,2-4,4}

x-2=1=>x=3=>y=4

x-2=-1=>x=1=>y=-4

x-2=-2=>x=0=>y=0

x-2=2=>x=4=>y=2

x-2=-4=>x=-2=>y=-1

x-2=4=>x=6=>y=1

vay cac cap so nguyen( x,y) la :(3,4),(1,-4),(0,0),(4,2),(-2,-1),(6,1)

x4

12

1 

Câu a:

\(\frac{x+5}{x+9}\) = \(\frac{x+4}{x+3}\)

(\(x\) + 5)(\(x+3\)) = (\(x+4\))(\(x+9\))

\(x^2\) + 3\(x\) + 5\(x\) + 15 = \(x^2\) + 9\(x\) + 4\(x\) + 36

\(x^2+3x+5x\) - \(x^2-9x\) - 4\(x\) = 36 - 15

(\(x^2-x^2\)) + (\(3x+5x\) - 9\(x-4x\)) = 21

0 + (8\(x\) - 9\(x\) - 4\(x\)) = 21

-\(x-4x\) = 21

-5\(x\) = 21

\(x\) = 21 : (-5)

\(x\) = - \(\frac{21}{5}\)

Vậy \(x=-\frac{21}{5}\)

Từ đẳng thức \(\frac{x}{2}=y=\frac{z}{3}\Rightarrow\frac{x}{2}=\frac{y}{1}=\frac{z}{3}\)

Đặt \(\frac{x}{2}=\frac{y}{1}=\frac{z}{3}=k\)

\(\Rightarrow\hept{\begin{cases}x=2k\\y=1k\\z=3k\end{cases}}\)

Khi đó : x - y + x = 240

       <=> 2k - k + 2k = 240

        <=> k + 2k = 240

        <=> 3k = 240

         <=> k = 80

=> \(\hept{\begin{cases}x=2.80=160\\y=80.1=80\\z=80.3=240\end{cases}}\)

sai đề nha phải là :x-y+z=240 nha

làm theo đề của m chữa lại nha

\(\frac{x}{2}=\frac{y}{1}=\frac{z}{3}\)  và \(x-y+z=240\)

áp dụng tích chất dãy tỉ số bằng nhau ta có:

\(\frac{x}{2}=\frac{y}{1}=\frac{z}{3}=\frac{x-y+z}{2-1+3}=\frac{240}{4}=60\)

\(\Rightarrow x=60.2=120\)

      \(y=60.1=60\)

      \(z=60.3=180\)

a) \(\frac{x-1}{x+5}=\frac{6}{7}\)

7( x - 1 ) = 6( x + 5 )

7x - 7 = 6x - 30

7x - 6x = -30 + 7

x = -23

b) \(\frac{x^2}{6}=\frac{24}{25}\)

\(x^2.25=6.24\)

\(x^2.25=144\)

\(x^2=\frac{144}{25}\)

\(x=\sqrt{\frac{144}{25}}\)

\(x=\frac{12}{5}\)

c) \(\frac{x-2}{x-4}=\frac{x+4}{x+7}\)

\(\left(x-2\right)\left(x+7\right)=\left(x+4\right)\left(x-4\right)\)

\(x^2+7x-2x-14=x^2-4x+4x-16\)

\(x^2+5x-14=x^2^{ }-16\)

\(x^2-x^2+5x=-16+14\)

\(5x=-2\)\(x=\frac{-2}{5}\)

\(\frac{x}{-7}=\frac{5}{-35}\)

\(\frac{x.5}{-35}=\frac{5}{-35}\)

=> x . 5 = 5

x = 5 : 5 

x = 1

sao trả lời có một câu mấy dậy bạn giúp mình với

a./ \(\frac{x}{5}=\frac{y}{7}=\frac{z}{4}=\frac{x-y+z}{5-7+4}=\frac{-10}{2}=-5\)

\(\Rightarrow x=-25;y=-35;z=-20\)

b./ \(\frac{x}{5}=\frac{y}{-4}=\frac{z}{-7}=\frac{x+y-z}{5-4-\left(-7\right)}=\frac{-40}{6}=-5\)

\(\Rightarrow x=-25;y=20;z=35\)