Sure, let’s break down the expression step by step:
Given the expression:
[tex]\[ \frac{x^2}{y^2} - 2 - \frac{3 y^2}{x^2} \][/tex]
### Step 1: Identify and understand each term in the expression.
1. The first term is [tex]\(\frac{x^2}{y^2}\)[/tex], which represents the ratio of [tex]\(x^2\)[/tex] to [tex]\(y^2\)[/tex].
2. The second term is [tex]\(-2\)[/tex], a constant.
3. The third term is [tex]\(-\frac{3y^2}{x^2}\)[/tex], which represents negative three times the ratio of [tex]\(y^2\)[/tex] to [tex]\(x^2\)[/tex].
### Step 2: Simplify each term as much as possible (if applicable).
- [tex]\(\frac{x^2}{y^2}\)[/tex]: This term is already simplified.
- [tex]\(-2\)[/tex]: This term is a constant and does not need further simplification.
- [tex]\(-\frac{3 y^2}{x^2}\)[/tex]: This term is already simplified.
### Step 3: Combine all the terms to form the simplified expression.
Putting it all together, we have the expression:
[tex]\[ \frac{x^2}{y^2} - 2 - \frac{3 y^2}{x^2} \][/tex]
### Step 4: Consider any restrictions or special cases (usually where variables cannot equal certain values to avoid division by zero).
- [tex]\(y \neq 0\)[/tex] because division by zero is undefined.
- [tex]\(x \neq 0\)[/tex] because division by zero is undefined in the term [tex]\(\frac{3 y^2}{x^2}\)[/tex].
Thus, the final expression in simplified form is:
[tex]\[ \frac{x^2}{y^2} - 2 - \frac{3 y^2}{x^2} \][/tex]
This is the expression as simplified as possible.
