Question

simplify the expression completely.

multiply the rational expressions:

\\(dfrac{x - 1}{16x + 4} cdot dfrac{4x + 1}{x^2 - 4}\\)

Explanation:

Step1: Factor all expressions

Factor $16x+4=4(4x+1)$, $x^2-4=(x-2)(x+2)$

Step2: Write the multiplication

$\frac{x-1}{4(4x+1)} \times \frac{4x+1}{(x-2)(x+2)}$

Step3: Cancel common factors

Cancel $(4x+1)$ from numerator and denominator:
$\frac{x-1}{4} \times \frac{1}{(x-2)(x+2)}$

Step4: Multiply remaining terms

$\frac{x-1}{4(x-2)(x+2)}$ or expand denominator: $\frac{x-1}{4(x^2-4)}=\frac{x-1}{4x^2-16}$

Answer:

$\frac{x-1}{4(x^2-4)}$ or $\frac{x-1}{4x^2-16}$