Answer
See below
Work Step by Step
$$\frac{6x^2+11x+4}{2x^2+3x-1}\div \frac{6x-8}{x+1}\\\frac{6x^2+11x+4}{2x^2+3x-1}\times\frac{x+1}{6x-8}\\\frac{6x^2+11x+4}{2x^2+3x-1}\times\frac{x+1}{2(3x-4)}\\\frac{(3x+4)(2x+1)}{2x^2+3x-1}\times\frac{x+1}{6x-8}\\\frac{(3x+4)(2x+1)(x+1)}{2(2x^2+3x-1)(3x-4)}\\$$