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The image shows the problem:

**Add or subtract as indicated and simplify if possible:**

\[
\frac{x}{x+2} - \frac{3 - x^2}{x^2 - 4}
\]

Let's go through the steps:

### Step 1: Factor the second denominator
The second denominator \(x^2 - 4\) is a difference of squares, so we can factor it:

\[
x^2 - 4 = (x - 2)(x + 2)
\]

Now, the expression becomes:

\[
\frac{x}{x+2} - \frac{3 - x^2}{(x-2)(x+2)}
\]

### Step 2: Rewrite the numerator of the second fraction
Notice that \(3 - x^2\) can be rewritten as:

\[
3 - x^2 = -(x^2 - 3)
\]

So the expression becomes:

\[
\frac{x}{x+2} - \frac{-(x^2 - 3)}{(x-2)(x+2)}
\]

Or equivalently:

\[
\frac{x}{x+2} + \frac{x^2 - 3}{(x-2)(x+2)}
\]

### Step 3: Combine the two fractions
To add or subtract fractions, they need to have the same denominator. The first fraction has a denominator of \(x+2\), and the second one has \((x-2)(x+2)\). Therefore, we multiply the numerator and denominator of the first fraction by \(x-2\) to make the denominators the same:

\[
\frac{x(x-2)}{(x-2)(x+2)} + \frac{x^2 - 3}{(x-2)(x+2)}
\]

### Step 4: Simplify the expression
Now, combine the numerators:

\[
\frac{x(x-2) + (x^2 - 3)}{(x-2)(x+2)}
\]

Expand \(x(x-2)\):

\[
x(x-2) = x^2 - 2x
\]

So the expression becomes:

\[
\frac{x^2 - 2x + x^2 - 3}{(x-2)(x+2)}
\]

Combine like terms in the numerator:

\[
\frac{2x^2 - 2x - 3}{(x-2)(x+2)}
\]

This is the simplified result. Comparing with the answer choices, the correct answer is:

\[
\boxed{a. \frac{2x^2 - 2x - 3}{x^2 - 4}}
\]

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Would you like more details on any step? 

Here are 5 related questions you might find useful:
1. How do you simplify rational expressions with polynomial numerators?
2. What are the common factoring techniques for quadratic expressions?
3. How do you identify the difference of squares in polynomial terms?
4. How can you add and subtract fractions with different denominators?
5. How do you recognize when to factor or expand algebraic expressions?

**Tip:** When dealing with rational expressions, always check for opportunities to factor the denominator and numerator to simplify the result.

Add or subtract as indicated and simplify if possible: (x / (x + 2)) - ((3 - x^2) / (x^2 - 4))

In this example, learn how to simplify the expression (x / (x + 2)) - ((3 - x^2) / (x^2 - 4)) using factoring techniques such as the difference of squares. This problem covers algebraic concepts, including rational expressions and common factoring methods.

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