Certainly! Let's simplify the expression step-by-step.
Given the expression:
[tex]\[ \frac{a^2}{b^2} - 3 + \frac{2 b^2}{a^2} \][/tex]
### Step 1: Analyze the Terms
The expression consists of three terms:
1. [tex]\(\frac{a^2}{b^2}\)[/tex]
2. [tex]\(-3\)[/tex]
3. [tex]\(\frac{2 b^2}{a^2}\)[/tex]
### Step 2: Identify Common Denominator (optional)
We can notice that [tex]\(\frac{a^2}{b^2}\)[/tex] and [tex]\(\frac{2 b^2}{a^2}\)[/tex] could be connected through their denominators, but it's not necessary for this simplification as we are looking for an overall simplification pattern.
### Step 3: Simplify (if needed) Individual Fractions
Each fraction here is already in its simplest form:
- [tex]\(\frac{a^2}{b^2}\)[/tex]
- [tex]\(\frac{2 b^2}{a^2}\)[/tex]
### Step 4: Combine and Reorganize
Now let's combine the fractions:
[tex]\[ \frac{a^2}{b^2} - 3 + \frac{2 b^2}{a^2} \][/tex]
In this case, simplifying further using algebraic identities or manipulations does not change the form of the expression in a meaningful way. Therefore, the simplified form of the given expression is:
[tex]\[ \frac{a^2}{b^2} - 3 + \frac{2 b^2}{a^2} \][/tex]
So, the expression remains:
[tex]\[ \frac{a^2}{b^2} - 3 + \frac{2 b^2}{a^2} \][/tex]
This is our simplified form.
