Question

Simplify \( \left( \frac{6x^2 - 4x}{2x} \right) \).

• A. (3x - 2)
• B. (3x + 2)
• C. (3x - 1)
• D. (3x + 1)

Hint:

An alternative method for simple denominators is to split the fraction: \( \frac{6x^2 - 4x}{2x} = \frac{6x^2}{2x} - \frac{4x}{2x} \). Then, simplify each term separately: \(3x - 2\). This can be faster for simple cases.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept
This problem requires simplifying an algebraic fraction. This is done by factoring the numerator and the denominator and then canceling out any common factors.
Step 2: Key Formula or Approach
The primary method is to find the greatest common factor (GCF) of the terms in the numerator and factor it out.
Step 3: Detailed Explanation
We are given the expression:
\[ \frac{6x^2 - 4x}{2x} \] First, let's look at the numerator, \(6x^2 - 4x\). The GCF of \(6x^2\) and \(4x\) is \(2x\).
Factor \(2x\) out of the numerator:
\[ 6x^2 - 4x = 2x(3x) - 2x(2) = 2x(3x - 2) \] Now, substitute this factored form back into the fraction:
\[ \frac{2x(3x - 2)}{2x} \] We can now cancel the common factor \(2x\) from the numerator and the denominator, assuming \(x \neq 0\).
\[ 3x - 2 \] Step 4: Final Answer
The simplified expression is \(3x - 2\).