Question

simplify.
\frac{\frac{x - 5}{2x - 14}}{\frac{5x^7}{7x - 49}}

Explanation:

Step1: Rewrite as multiplication (divide by fraction = multiply by reciprocal)

The complex fraction \(\frac{\frac{x - 5}{2x - 14}}{\frac{5x^{7}}{7x - 49}}\) is equivalent to \(\frac{x - 5}{2x - 14} \times \frac{7x - 49}{5x^{7}}\)

Step2: Factor denominators and numerators

Factor \(2x - 14 = 2(x - 7)\) and \(7x - 49 = 7(x - 7)\)
So now we have \(\frac{x - 5}{2(x - 7)} \times \frac{7(x - 7)}{5x^{7}}\)

Step3: Cancel common factors

Cancel out the common factor \((x - 7)\) from the numerator and denominator
We get \(\frac{x - 5}{2} \times \frac{7}{5x^{7}}\)

Step4: Multiply the fractions

Multiply the numerators: \((x - 5) \times 7 = 7(x - 5)\)
Multiply the denominators: \(2 \times 5x^{7}=10x^{7}\)
So the simplified form is \(\frac{7(x - 5)}{10x^{7}}\) or \(\frac{7x - 35}{10x^{7}}\)

Answer:

\(\frac{7(x - 5)}{10x^{7}}\) (or \(\frac{7x - 35}{10x^{7}}\))