Question

simplify.
\\(\dfrac{\dfrac{x - 2}{3x - 21}}{\dfrac{2x^7}{7x - 49}}\\)

Explanation:

Step1: Rewrite as multiplication

Dividing by a fraction is multiplying by its reciprocal, so:
$$\frac{\frac{x - 2}{3x - 21}}{\frac{2x^7}{7x - 49}}=\frac{x - 2}{3x - 21}\times\frac{7x - 49}{2x^7}$$

Step2: Factor denominators and numerators

Factor out common terms: \(3x - 21 = 3(x - 7)\), \(7x - 49 = 7(x - 7)\)
So the expression becomes:
$$\frac{x - 2}{3(x - 7)}\times\frac{7(x - 7)}{2x^7}$$

Step3: Cancel common factors

Cancel out \((x - 7)\) from numerator and denominator:
$$\frac{x - 2}{3}\times\frac{7}{2x^7}$$

Step4: Multiply the fractions

Multiply the numerators and denominators:
$$\frac{7(x - 2)}{6x^7}$$

Answer:

\(\frac{7(x - 2)}{6x^7}\)