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 \(x\ne-2;-3\)
\(\Leftrightarrow\left(x+2\right)\left(x-2\right)=\left(x-1\right)\left(x+3\right)\)
\(\Leftrightarrow x^2-4=x^2+2x-3\)
\(\Leftrightarrow x^2-x^2+2x=-3+4\)
\(\Leftrightarrow2x=1\)
\(\Leftrightarrow x=\frac{1}{2}\)
