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