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
