Question

perform the operation and simplify.
\\(\frac{2x^2 - 10}{x + 1} \cdot \frac{x - 4}{4x^2 - 20}\\)
\\(\frac{x - \boxed{?}}{\boxed{\quad}(x + \boxed{\quad})}\\)

Explanation:

Step1: Factor numerators/denominators

$\frac{2(x^2 - 5)}{x + 1} \cdot \frac{x - 4}{4(x^2 - 5)}$

Step2: Cancel common factors

$\frac{2}{x + 1} \cdot \frac{x - 4}{4}$

Step3: Multiply remaining terms

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

Step4: Simplify the constant

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

Answer:

The missing values are: $\boldsymbol{4}$ (in the green box), $\boldsymbol{2}$ (first beige box), $\boldsymbol{1}$ (second beige box). The fully simplified expression is $\frac{x - 4}{2(x + 1)}$