[latex] frac{3}{x-2} = frac{4}{x-5} [/latex]

[latex] frac{3(x-5)-4(x-2)}{(x-2)(x-5)} =0;[/latex][latex]left { {{3(x-5)-4(x-2) = 0} atop {(x-2)(x-5) eq 0}} ight. ;[/latex][latex] left { {{(3-4)x=3*5-4*2} atop {x eq 2},and,x eq 5} ight. ; left { {{x=-7} atop {x eq 2},and,x eq 5}} ight. ;x=-7[/latex]Answer: -7.