What is the quotient

[(x^2) / (2x^2-9x + 4)] / [(2x^2 + 14x + 24) / (4x + 4)]

2 answers

2x^2-9x+4 = (2x-1)(x-4)
2x^2+14x+24 = 2(x+4)(x+3)

so, what you have is

x^2 / (2x-1)(x-4) * 4(x+1) / 2(x+4)(x+3)

hm. no factors cancel but the 2's, so we wind up with

2x^2(x+1) / (2x-1)(x-4)(x+4)(x+3)
= (2x^3 + 2x^2)/(2x^4+5x^3-35x^2-80x+48)

Not very simple.
Steve, I am sorry, I left out a number:
What is the quotient?
[(x^2 -16) / (2x^2-9x + 4)] / [(2x^2 + 14x + 24) / (4x + 4)]