Final answer:
To simplify the expression (x² + 3x - 28)/(x² - 7x + 12), factor both the numerator and the denominator and cancel the common term, resulting in the simplified form (x + 7)/(x - 3).
Step-by-step explanation:
To simplify the expression x² + 3x - 28/x² - 7x + 12, we first factor both the numerator and the denominator of the rational expression.
For the numerator x² + 3x - 28, the factors are (x + 7)(x - 4), since (x + 7)(x - 4) expands to x² + 3x - 28.
For the denominator x² - 7x + 12, the factors are (x - 3)(x - 4), as (x - 3)(x - 4) expands to x² - 7x + 12.
Thus, our expression simplifies to:
((x + 7)(x - 4))/((x - 3)(x - 4))
We can now cancel out the common term (x - 4) from the numerator and denominator:
(x + 7)/(x - 3)
This is the simplified form of the given expression.