Simplify x² - 4¼x²: Combining Like Terms with Fractions

To solve this problem, we'll follow these steps:

• Step 1: Identify the coefficients for each term.
• Step 2: Combine the coefficients using arithmetic rules for signed numbers.
• Step 3: Write the result in terms of $x^2$.

Now, let's work through each step:
Step 1: The expression has the terms $+x^2$ and $-4 \frac{1}{4} x^2$. Here, the coefficients are $+1$ for the first term and $-4 \frac{1}{4}$ for the second term, which is equivalent to $-4.25$.

Step 2: We combine the coefficients $+1$ and $-4.25$ as follows:
$1 - 4.25 = -3.25$.

Step 3: Attach the coefficient back to $x^2$, which results in:
$-3.25x^2$ or $-3\frac{1}{4}x^2$.

Therefore, the solution to the problem is $-3\frac{1}{4}x^2$.