x=7/2

x=7/2

P/s : Vì bạn lớp 7 nên mình giải chi tiết nha!

Có \(\frac{x-1}{x+2}=\frac{x-2}{x+3}\Leftrightarrow\left(x-1\right)\left(x+3\right)=\left(x+2\right)\left(x-2\right)\)

\(\Leftrightarrow x\left(x+3\right)-1\left(x+3\right)=x\left(x-2\right)+2\left(x-2\right)\)

\(\Leftrightarrow x^2+3x-x-3=x^2-2x+2x-4\)

\(\Leftrightarrow x^2+\left(3x-x\right)-3=x^2+\left(2x-2x\right)-4\)

\(\Leftrightarrow x^2+2x-3=x^2-4\Leftrightarrow x^2-x^2+2x=3-4=-1\)

\(=\left(x^2-x^2\right)+2x=-1\Leftrightarrow2x=1\Leftrightarrow x=1\div2=\frac{1}{2}\)

\(\frac{x-1}{x+2}=\frac{x-2}{x+3}\) đkxđ \(x\ne-2;-3\)

\(\Leftrightarrow\left(x+2\right)\left(x-2\right)=\left(x-1\right)\left(x+3\right)\)

\(\Leftrightarrow x^2-4=x^2+2x-3\)

\(\Leftrightarrow x^2-x^2+2x=-3+4\)

\(\Leftrightarrow2x=1\)

\(\Leftrightarrow x=\frac{1}{2}\)

a) - 0,52 : x = - 9,36 : 16,38

- 0,52 : x = \(-\frac{4}{7}\)

\(x=\left(-0,52\right):\left(-\frac{4}{7}\right)=\frac{91}{100}=0,91\)

b) \(\frac{4\frac{1}{4}}{2\frac{7}{8}}=\frac{x}{1,61}\)

\(\frac{\frac{17}{4}}{\frac{23}{8}}=\frac{x}{1,61}\)

\(\frac{x}{1,61}=\frac{34}{23}\)

\(x=\frac{34}{23}.1,61=2,38\)

Bài 1:

a) \(\frac{x}{-15}=\frac{-60}{x}\Rightarrow x^2=\left(-60\right).\left(-15\right)=900\Rightarrow x=\orbr{\begin{cases}30\\-30\end{cases}}\)

Bài 2: Đặt \(\frac{x}{4}=\frac{y}{7}=k\Rightarrow x=4k;y=7k\)

\(\Rightarrow xy=4k.7k=28k^2=112\)

\(\Rightarrow k^2=4\Rightarrow k=\pm2\)

\(\Rightarrow\orbr{\begin{cases}x=4.2=8\\x=-4.2=-8\end{cases}}\)

Và \(\orbr{\begin{cases}y=7.2=14\\y=-7.2=-14\end{cases}}\)

Bài 3: \(1\frac{1}{3}:0,8=\frac{2}{3}:\left(0,1x\right)\)

\(\Rightarrow\frac{4}{3}:\frac{4}{5}=\frac{2}{3}:\frac{1}{10}x\Rightarrow\frac{5}{3}=\frac{2}{3}:\frac{1}{10}x\)

\(\Rightarrow\frac{1}{10}x=\frac{2}{5}\Rightarrow x=4\)

Mk trả lời nốt bài 4 hộ bn MMS_Hồ Khánh Châu nha:
Bài 4:
Gọi x là giá trị chung của 2 phân số trên.
Ta có: \(\frac{a}{b}=\frac{c}{d}=x\)
\(\Rightarrow a=x.b \)
      \(c=x.d\)
Ta lại có: 
\(\frac{a+c}{b+d}=\frac{x.b+x.d}{b+d}=\frac{x.\left(b+d\right)}{b+d}=x\)
Và \(\frac{a}{b}=x\)
\(\Rightarrow\frac{a}{b}=\frac{a+c}{b+d}\)
Vậy \(\frac{a}{b}=\frac{a+c}{b+d}\)
Hk tốt nha

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

\(\Rightarrow x^2+2x-3=x^2-4\)

\(\Rightarrow2x=-1\)

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

b)\(\frac{37-x}{x+13}=\frac{3}{7}\)\(\Rightarrow7\left(37-x\right)=3\left(x+13\right)\)

\(\Rightarrow259-7x=3x+39\)

\(\Rightarrow10x=220\)

\(\Rightarrow x=22\)

\(\frac{4\frac{1}{4}}{2\frac{7}{8}}=\frac{x}{1,61}\)

\(\Leftrightarrow\frac{\frac{17}{4}}{\frac{23}{8}}=\frac{x}{1,61}\)

\(\Leftrightarrow\frac{34}{23}=\frac{x}{1,61}\)

\(\Leftrightarrow x=\frac{34}{23}.1,61\)

\(\Leftrightarrow x=\frac{119}{50}\)

a) \(\frac{3x-2}{1\frac{2}{5}}=\frac{2\frac{3}{7}}{2\frac{3}{5}}\Rightarrow3x-2=1.\frac{2}{5}.\frac{2\frac{3}{7}}{2\frac{3}{5}}=\frac{7}{5}.\frac{17}{7}.\frac{5}{13}\)

\(3x-2=\frac{17}{13}\Rightarrow3x=2+\frac{17}{13}=\frac{43}{13}\Rightarrow x=\frac{43}{39}.\)

b) \(\frac{x}{0,16}=\frac{9}{x}\Rightarrow x^2=9.0,16=1,44\Rightarrow x=\pm1,2\)

\(\text{a)}\frac{37-x}{x+13}=\frac{3}{7}\)

\(\Leftrightarrow3\left(x+13\right)=7\left(37-x\right)\)

\(\Leftrightarrow3x+39=259-7x\)

\(\Leftrightarrow3x+7x=259-39\)

\(\Leftrightarrow10x=220\)

\(\Leftrightarrow x=22\)

\(\text{b)}\frac{x+4}{20}=\frac{5}{x+4}\)

\(\Leftrightarrow\left(x+4\right)^2=100\)

\(\Leftrightarrow\orbr{\begin{cases}x+4=10\\x+4=-10\end{cases}\Leftrightarrow}\orbr{\begin{cases}x=6\\x=-14\end{cases}}\)