You provided the expression:

$\frac{x^2 - 4x + 6x^3}{2x}$

To simplify this expression, let's go step by step:

Step 1: Split the terms

We can split the fraction into separate terms, dividing each term in the numerator by $2x$:

$\frac{x^2}{2x} - \frac{4x}{2x} + \frac{6x^3}{2x}$

Step 2: Simplify each term

• For the first term: $\frac{x^2}{2x} = \frac{1}{2}x$
• For the second term: $\frac{4x}{2x} = 2$
• For the third term: $\frac{6x^3}{2x} = 3x^2$

Step 3: Combine the simplified terms

Putting everything together, the simplified expression is:

$\frac{1}{2}x - 2 + 3x^2$

Thus, the simplified expression is:

$3x^2 + \frac{1}{2}x - 2$

Would you like more details on any of the steps?

Related questions:

1. How would you simplify $\frac{3x^2 - 5x + 2x^3}{x}$?
2. Can you solve the equation $\frac{x^2 - 4x + 6x^3}{2x} = 0$?
3. What happens if you multiply $\frac{x^2 - 4x + 6x^3}{2x}$ by $x$?
4. How do you simplify $\frac{5x^3 + 2x^2 - x}{x}$?
5. How do you factor the expression $3x^2 + \frac{1}{2}x - 2$?

Tip:

When simplifying rational expressions, always check for common factors in both the numerator and denominator that you can cancel out.