\(\frac{x-20}{x-10}=\frac{x+40}{x+70}\)
\(\Rightarrow\left(x-20\right)\left(x+70\right)=\left(x-10\right)\left(x+40\right)\)
\(\Rightarrow x^2+70x-20x-1400=x^2+40x-10x-400\)
\(\Rightarrow x^2+70x-20x-x^2-40x+10x=1400-400\)
\(\Rightarrow20x=1000\Rightarrow x=50\)