Question

question 9
2 pts
simplify each expression.
\\(\frac{20n - 20}{6n^2} \div \frac{8n - 8}{6n^2}\\)
numerator / denominator = /

Explanation:

Step1: Rewrite division as multiplication

To divide by a fraction, we multiply by its reciprocal. So, $\frac{20n - 20}{6n^2} \div \frac{8n - 8}{6n^2}$ becomes $\frac{20n - 20}{6n^2} \times \frac{6n^2}{8n - 8}$.

Step2: Factor numerators

Factor out the greatest common factor from the numerators: $20n - 20 = 20(n - 1)$ and $8n - 8 = 8(n - 1)$. Now the expression is $\frac{20(n - 1)}{6n^2} \times \frac{6n^2}{8(n - 1)}$.

Step3: Cancel common factors

We can cancel out the common factors $6n^2$ and $(n - 1)$ from the numerator and the denominator. This leaves us with $\frac{20}{8}$.

Step4: Simplify the fraction

Simplify $\frac{20}{8}$ by dividing both the numerator and the denominator by their greatest common divisor, which is 4. So, $\frac{20 \div 4}{8 \div 4} = \frac{5}{2}$.

Answer:

Numerator: 5, Denominator: 2 (in the form [Numerator]/[Denominator] = 5/2)