\(\frac{x-2}{x-1}=\frac{x+4}{x+7}\)
\(\Rightarrow\left(x-2\right).\left(x+7\right)=\left(x-1\right).\left(x+4\right)\)
\(\left(x-2\right)x+\left(x-2\right)7=\left(x-1\right)x+\left(x-1\right)4\\ x^2-2x+7x-14=x^2-x+4x-4\\ \)
\(x^2-\left(2x-7x\right)-14=x^2-\left(x-4x\right)-4\)
\(x^2-x^2-\left(-5x\right)=-3x-4+14\)
\(5x=-3x+10\\ 5x+3x=10\\ 8x=10\\ x=10:8\\ x=1,25\)