Simplify (-x²)-(-4⁴/₅x²): Subtracting Negative Square Terms

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

• Step 1: Investigate the given expression: $(-x^2)-(-4\frac{4}{5}x^2)$.
• Step 2: Convert the subtraction of negatives to addition: $-x^2 + 4\frac{4}{5}x^2$.
• Step 3: Combine like terms: the terms share the common factor $x^2$.
• Step 4: Simplify the coefficients: The expression becomes $(4\frac{4}{5} - 1)x^2$.
• Step 5: Simplify the numerical operation: transforming $4\frac{4}{5}$ to $\frac{24}{5}$, we get $( \frac{24}{5} - 1)x^2 = ( \frac{24}{5} - \frac{5}{5} )x^2$.
• Step 6: Continue simplifying: $( \frac{19}{5} )x^2$, equivalent to $3\frac{4}{5}x^2$.

Now, let's execute these steps with detailed explanations:

Step 1: The expression involves subtracting $-4\frac{4}{5}x^2$ from $-x^2$. Initially, handle the signs carefully by recognizing that subtracting a negative is equivalent to adding the positive.

Step 2: Transform the expression as follows: $(-x^2)-(-4\frac{4}{5}x^2) \Rightarrow -x^2 + 4\frac{4}{5}x^2$.

Step 3: Here, both terms $-x^2$ and $4\frac{4}{5}x^2$ involve $x^2$. Write them as combined like terms.

Step 4: The coefficients are $-1$ and $4\frac{4}{5}$. Combine them: $-1 + 4\frac{4}{5} = 3\frac{4}{5}$.

Step 5: This simplifies the expression to $3\frac{4}{5}x^2$, shown through straightforward arithmetic with like terms.

Therefore, the simplified expression is $\boxed{3\frac{4}{5}x^2}$, matching the correct answer choice.