The given equation is:

$\frac{4x + x - 4}{3} = 3$

Step 1: Determine the Least Common Denominator (LCD)

Here, the only denominator is 3, so the LCD is simply:

$\text{LCD} = 3$

Step 2: Multiply the Entire Equation by the LCD

Multiplying each term by 3 gives:

$3 \cdot \frac{4x + x - 4}{3} = 3 \cdot 3$

This simplifies to:

$4x + x - 4 = 9$

Step 3: Simplify and Transform the Equation into General Quadratic Form

Combine like terms:

$5x - 4 = 9$

Next, add 4 to both sides to isolate the $x$ term:

$5x = 13$

Finally, divide both sides by 5:

$x = \frac{13}{5}$

Analysis

In this case, the equation simplifies to a linear equation rather than a quadratic one. Therefore, the general quadratic form is not applicable here. The solution is simply $x = \frac{13}{5}$.

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Do you need more details or have any questions? Here are some related questions you might find interesting:

1. How do you determine the LCD when dealing with multiple fractions?
2. How can you verify if a solution to an equation is correct?
3. What are the differences between linear and quadratic equations?
4. How do you convert linear equations into standard form?
5. What strategies are useful for solving more complex algebraic equations?

Tip: Always simplify the equation step-by-step to identify whether it's linear or quadratic!