This appears to be intended to be an exercise in factoring:
#15-14x-8x^2 = (5+2x)(3-4x)#
#4x^2+4x-15 = (2x-3)(2x+5)#
#4x^2+13x -12 = (4x-3)(x+4)#
#3x^2+16x+5 = (3x+1)(x+5)#
Returning to the original expression:
#(15-14x-8x^2)/(4x^2+4x-15) div (4x^2+13x -12)/(3x^2+16x+5)#
#=##color(white)("XXXX")##(15-14x-8x^2)/(4x^2+4x-15) *
(3x^2+16x+5) /(4x^2+13x -12)#
#=##color(white)("XXXX")##((5+2x)(3-4x))/((2x-3)(2x+5))*((3x+1)(x+5))/((4x-3)(x+4))#
#=##color(white)("XXXX")##(cancel((5+2x))(3-4x))/((2x-3)cancel((2x+5)))*((3x+1)(x+5))/((4x-3)(x+4))#
#=##color(white)("XXXX")##(cancel((3-4x))^(-1))/((2x-3))*((3x+1)(x+5))/(cancel((4x-3))(x+4))#
#=##color(white)("XXXX")##-((3x+1)(x+5))/((2x-3)(x+4))#
or
#=##color(white)("XXXX")##(3x^2+16x+5)/(2x^2+5x-12)#
