Question

algebra: concepts and connections - plc
adding and subtracting rational expressions
what is the value of the rational expression \\(\frac{2x^2 + 5x + 9}{x^2 + 2x - 1}\\) when \\(x = -2\\)?
options: -7, 9, -9, 7

Explanation:

Step1: Substitute $x=-2$ into numerator

Calculate $2x^2+5x+9$:
$$2(-2)^2 + 5(-2) + 9 = 2(4) -10 +9 = 8 -10 +9 =7$$

Step2: Substitute $x=-2$ into denominator

Calculate $x^2+2x-1$:
$$(-2)^2 + 2(-2) -1 = 4 -4 -1 = -1$$

Step3: Divide numerator by denominator

$$\frac{7}{-1} = -7$$

Answer:

-7