The given mathematical expression appears to be incomplete or incorrectly formatted. Based on standard mathematical notation, a possible correction is:

[tex]\[ \frac{x^2 - b^2}{a + b^2} \][/tex]

If the intended meaning was different, please provide additional context or clarification.



Answer :

Sure, let's go through the simplification of the given expression step-by-step:

We start with the expression:

[tex]\[ \frac{x^2 - b^2}{a + b^2} \][/tex]

### Step 1: Recognize the Difference of Squares

The numerator [tex]\(x^2 - b^2\)[/tex] is a difference of squares. Recall the difference of squares formula:

[tex]\[ x^2 - b^2 = (x + b)(x - b) \][/tex]

Thus, we can rewrite the numerator as:

[tex]\[ (x + b)(x - b) \][/tex]

### Step 2: Rewrite the Initial Expression

Substitute the factored form of the numerator back into the original expression:

[tex]\[ \frac{(x + b)(x - b)}{a + b^2} \][/tex]

### Step 3: Simplify the Expression

Currently, there are no common factors in the numerator and denominator that can be cancelled since the denominator [tex]\(a + b^2\)[/tex] does not share any common terms with the factored form [tex]\((x + b)(x - b)\)[/tex].

Therefore, the simplified form of the expression is:

[tex]\[ \frac{(x + b)(x - b)}{a + b^2} \][/tex]

### Step 4: Confirm the Simplified Form

The final simplified form of the expression, step-by-step, is:

[tex]\[ \frac{x^2 - b^2}{a + b^2} \][/tex]

### Step 5: Present the Result

So, the simplified form of the given expression is:

[tex]\[ \frac{-b^2 + x^2}{a + b^2} \][/tex]

Notice that [tex]\(-b^2 + x^2\)[/tex] is algebraically equivalent to [tex]\(x^2 - b^2\)[/tex], which matches our original term.

Thus, the final answer is:

[tex]\[ \frac{-b^2 + x^2}{a + b^2} \][/tex]

This completes our step-by-step solution.