Triangles KPQ and KJL are similar because the line segments PQ and JL are parallel. This means corresponding parts of the triangles occur in the same ratio. In particular,
[tex]\dfrac{x-6}{(x-6)+3}=\dfrac x{x+5}[/tex]
Solve for [tex]x[/tex]:
[tex]\dfrac{x-6}{x-3}=\dfrac x{x+5}[/tex]
[tex](x-6)(x+5)=x(x-3)[/tex]
[tex]x^2-x-30=x^2-3x[/tex]
[tex]2x=30[/tex]
[tex]\boxed{x=15}[/tex]
