AO/OC=BO/OD

3x-1/5x-3=2x+1/6x-5

(3x-1)(6x-5)= (2x+1) (5x-3)

18x²-15x-6x+5=10x²-6x+5x-3

18x²-21x+5=10x²-x-3

18x²-21x+5-10x²+x+3=0

8x²-20x+8=0

4(2x²-5x+2)=0

2x²-5x+2=0

2x²-4x-x+2=0

2x(x-2)-1(x-2)=0

(x-2)(2x-1)=0

x-2=0

x=2

Or, 2x-1=0

2x=1

x=1/2

But x=1/2 is not possible

So x=2