Simplify quantity 4 x squared plus 12 x minus 16 all over quantity 2x plus 10 over quantity 6 x plus 24 over quantity x squared plus 9x plus 20.

In this item, we are to simplify the following expressions,
                    (4x² + 12x - 16) / (2x + 10)   ÷ (6x + 24)/(x² + 9x + 20)

We can transform the expression such that instead of division, the operation involved now will be multiplication by interchanging the numerator and denominator of the second expression,
 
               (4x² + 12x - 16) / (2x + 10)    x   ( x² + 9x + 20) / (6x + 24)

We factor out both the numerator and denominator of the expressions,
 
              (x + 4)(x -1)(4) / (2)(x + 5)    x    (x + 5)(x + 4) / (6)(x + 4)

Then, we cancel the like terms which appears in both numerator and denominator and we will be left with,
                           (2)(x + 4)(x - 1)
                            2(x² + 3x - 4)
                             2x² + 6x - 8