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Evaluate the limit


    \[ \lim_{x \to a} \frac{x^2 - a^2}{x^2 + 2ax + a^2}, \qquad \text{for } a \neq 0. \]

Here we have a quotient of continuous functions (since the numerator and denominator are polynomials and all polynomials are continuous). Further, since a \neq 0, the denominator is non-zero. Thus, the quotient is continuous and we compute the limit as,

    \[ \lim_{x \to a} \frac{x^2 - a^2}{x^2 + 2ax + a^2} = \frac{0}{4a^2} = 0. \]

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