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[tex]\\ \sf\longmapsto \dfrac{2x+3}{x-3}=\dfrac{3}{5}[/tex]
[tex]\\ \sf\longmapsto 5(2x+3)=3(x-3)[/tex]
[tex]\\ \sf\longmapsto 10x+15=3x-9[/tex]
[tex]\\ \sf\longmapsto 10x-3x=-9-15[/tex]
[tex]\\ \sf\longmapsto 7x=-24[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{-24}{7}[/tex]