To divide these, you simply multiply the first fraction by the reciprocal of the second, meaning you flip the numerator and denominator. That means that we have (2x^2-5x-3)*(6x^2+11x-10)/(4x^2+12x+5)*(3x^2-11x+6). I'll factor one of the expressions, and I challenge you to do the rest!
For 2x^2-5x-3, we see that 2 multiplies the x^2, so we multiply 2 by -3 to get -6. We have to find 2 numbers that add to -5 but multiply to -6. With a bit of guess and check, we end up with -6 and 1, resulting in 2x^2-6x+x-3
= 2x(x-3)+1(x-3)= (2x+1)(x-3). Factor the rest, and you should have your answer! Good luck!