\(\frac{2x+2}{5x-3}=\frac{2x+12}{5x+18}=\frac{\left(2x+2\right)-\left(2x+12\right)}{\left(5x-3\right)-\left(5x+18\right)}=\frac{2x+2-2x-12}{5x-3-5x-18}=\frac{-10}{-21}=\frac{10}{21}\)=\(\frac{10}{21}\)
=>\(\frac{2x-2}{5x-3}=\frac{10}{21}\)
=>(2x-2).21=(5x-3).10
=>42x-42=50x-30
=>50x - 42x=-30+42
=> 8x=8
=>x=1