\(\frac{x-2}{x-1}=\frac{x+4}{x+7}\)
\(\Rightarrow\left(x-2\right).\left(x+7\right)=\left(x-1\right).\left(x+4\right)\)
\(\Rightarrow x^2+7x-2x-14=x^2+4x-x-4\)
\(\Rightarrow x^2+5x-14=x^2+3x-4\)
\(\Rightarrow x^2+5x-14-x^2-3x+4=0\)
\(\Rightarrow2x-10=0\)
\(\Rightarrow2x=0+10\)
\(\Rightarrow2x=10\)
\(\Rightarrow x=10:2\)
\(\Rightarrow x=5\)
Vậy \(x=5.\)
Chúc bạn học tốt!