Simplify the given expression6k-2
______
3k-1

To simplify the expression \(\frac{6k - 2}{3k - 1}\), let's follow these steps:

1. Factor the numerator and the denominator if possible.

   - The numerator \(6k - 2\) has a common factor of 2:
     \[
     6k - 2 = 2(3k - 1)
     \]

   - The denominator \(3k - 1\) cannot be factored further, so it stays as is.

2. Rewrite the expression using the factored form:
   \[
   \frac{6k - 2}{3k - 1} = \frac{2(3k - 1)}{3k - 1}
   \]

3. Cancel out the common factor \((3k - 1)\) from the numerator and the denominator, provided that \(3k - 1 \neq 0\) (i.e., \(k \neq \frac{1}{3}\)):

   \[
   \frac{2(3k - 1)}{3k - 1} = 2
   \]

So, the simplified expression is:
\[
2
\]

Would you like more details or have any questions?

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Here are five related questions:

1. How would the simplification change if the expression had different coefficients?
2. What happens if \(k = \frac{1}{3}\)? 
3. How do you factor a quadratic expression?
4. Can you simplify an expression when the denominator is zero?
5. What are common mistakes made when simplifying rational expressions?

**Tip:** Always check if factors in the numerator and denominator can be canceled out, but first ensure that the denominator is not zero.

Simplify the given expression 6k-2 / 3k-1

Learn how to simplify the rational expression (6k - 2) / (3k - 1) with a step-by-step explanation. This problem covers key algebraic concepts, including factoring and canceling common terms. Suitable for students in Grades 8-10.

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