Now compute $ \frac{a^2 + 4b^2}{a^2 - 4b^2} $. Since $ b = 0 $, this becomes:

["Now Compute $ \frac{a^2 + 4b^2}{a^2 - 4b^2} $ When $ b = 0 $: A Clear Explanation", "When solving mathematical expressions like $ \frac{a^2 + 4b^2}{a^2 - 4b^2} $, it's essential to carefully evaluate the values of variables involved. A common starting point in such problems is to substitute known values to simplify the expression. In this case, we are given that $ b = 0 $, which significantly impacts the form of the expression.", "Start by substituting $ b = 0 $ into the numerator and denominator:", "Numerator:\n$$\na^2 + 4b^2 = a^2 + 4(0)^2 = a^2 + 0 = a^2\n$$", "Denominator:\n$$\na^2 - 4b^2 = a^2 - 4(0)^2 = a^2 - 0 = a^2\n$$", "Now substitute these simplified results back into the original expression:\n$$\n\frac{a^2 + 4b^2}{a^2 - 4b^2} = \frac{a^2}{a^2}\n$$", "Since $ a^2 <br/>\neq 0 $ (assuming $ a <br/>\neq 0 $), the expression simplifies cleanly:\n$$\n\frac{a^2}{a^2} = 1\n$$", "Therefore, when $ b = 0 $, the value of $ \frac{a^2 + 4b^2}{a^2 - 4b^2} $ becomes 1.", "This example highlights the importance of substitution and simplification in algebraic computation. Even in seemingly complex rational expressions, plugging in known values—especially zero—can resolve indeterminate forms and reveal clear results.", "In summary:\nFor $ b = 0 $,\n$$\n\frac{a^2 + 4b^2}{a^2 - 4b^2} = 1, \quad \ ext{provided } a <br/>\ne 0.\n$$", "This clear outcome is especially useful in solving equations, simplifying rational expressions, and analyzing limit behavior in calculus, where direct substitution after clearing domains supports accurate evaluations."]