Question

what is the value of \\(\frac{3a^2 + 2b^2 - a - 4}{4a^2 + b}\\) when \\(a = -1\\) and \\(b = 3\\)?
options:
\\(-\frac{19}{7}\\)
\\(-\frac{19}{16}\\)
\\(\frac{29}{35}\\)
\\(\frac{17}{7}\\)

Explanation:

Step1: Substitute $a=-1$, $b=3$

Substitute values into the expression:
$$\frac{3(-1)^2 + 2(3)^2(-1) - 4}{4(-1)^2 + 3}$$

Step2: Calculate exponents first

Simplify squared terms:
$$\frac{3(1) + 2(9)(-1) - 4}{4(1) + 3}$$

Step3: Compute multiplications

Calculate all multiplicative terms:
$$\frac{3 - 18 - 4}{4 + 3}$$

Step4: Compute numerator and denominator

Sum numerator and denominator separately:
$$\frac{3 - 22}{7} = \frac{-19}{7}$$

Answer:

$\boldsymbol{-\frac{19}{7}}$ (Option A)