\(\frac{x-2}{x-1}=\frac{x+4}{x+7}\)
\(\Rightarrow\left(x-2\right)\left(x+7\right)=\left(x-1\right)\left(x+4\right)\)
\(\Rightarrow x\left(x+7\right)-2\left(x+7\right)=x\left(x+4\right)-\left(x+4\right)\)
\(\Rightarrow x^2+7x-\left(2x+14\right)=x^2+4x-x-4\)
\(\Rightarrow x^2+7x-2x-14=x^2+4x-x-4\)
\(\Rightarrow x^2+5x-14=x^2+3x-4\)
\(\Rightarrow x^2+5x-3x=x^2-4+14\)
\(\Rightarrow x^2+2x=x^2+10\)
\(\Rightarrow2x=10\)
\(\Rightarrow x=5\)
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