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