Find the number of terms in `2x^(2)-(3)/(x)+(5)/(x^(2))+9`.

Options

A. 1
B. 2
C. 3
D. 4

Answer

To find the number of terms in the expression \(2x^{2} - \frac{3}{x} + \frac{5}{x^{2}} + 9\), we will follow these steps:

### Step 1: Identify each term in the expression.

The expression is:
\[ 2x^{2} - \frac{3}{x} + \frac{5}{x^{2}} + 9 \]

### Step 2: Break down the expression into individual terms.

1. The first term is \(2x^{2}\).
2. The second term is \(-\frac{3}{x}\).
3. The third term is \(\frac{5}{x^{2}}\).
4. The fourth term is \(9\).

### Step 3: Count the number of distinct terms.

Now, we will count the distinct terms identified:
- \(2x^{2}\) (1st term)
- \(-\frac{3}{x}\) (2nd term)
- \(\frac{5}{x^{2}}\) (3rd term)
- \(9\) (4th term)

### Conclusion:

Adding these up, we find that there are a total of 4 distinct terms in the expression.

Thus, the number of terms in the expression \(2x^{2} - \frac{3}{x} + \frac{5}{x^{2}} + 9\) is **4**.

### Final Answer:
The number of terms is **4**.

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