Question

1. \\(\frac{21x^3 - 84x}{14x^2 - 35x}\\)

Explanation:

Step1: Factor numerator and denominator

Factor out common terms:
Numerator: \(21x^3 - 84x = 21x(x^2 - 4) = 21x(x - 2)(x + 2)\) (using difference of squares \(a^2 - b^2=(a - b)(a + b)\))
Denominator: \(14x^2 - 35x = 7x(2x - 5)\)

Step2: Simplify the fraction

Cancel common factors (note \(x
eq0\) to avoid division by zero):
\(\frac{21x(x - 2)(x + 2)}{7x(2x - 5)} = \frac{3(x - 2)(x + 2)}{2x - 5}\) (divided 21 by 7, canceled \(x\))

Answer:

\(\frac{3(x^2 - 4)}{2x - 5}\) (or expanded \(\frac{3x^2 - 12}{2x - 5}\))