<s>[INST] What am I doing wrong? Finding a limit as $x$ approaches $0$ $$\lim_{x\to 0} {a-\sqrt{a^2-x^2}\over x^2} =$$
$${a-\sqrt{a^2-x^2}\over x^2}\cdot{a+\sqrt{a^2-x^2}\over a+\sqrt{a^2-x^2}} = $$
$$a^{2} - a^{2} - x^{2}\over ax^{2} + x^{2}\sqrt{a^{2}-x^{2}} $$
$$-x^{2}\over ax^{2}+x^{2}\sqrt{a^{2}-x^{2}}$$
$$-1\over a+\sqrt{a^{2}-x^{2}}$$  
Can anyone tell me where I'm wrong? 
 [/INST] Third equality $$\left (a - \sqrt{a^2-x^2}\right )\left (a+\sqrt{a^2+x^2}\right ) \color{blue}{=x^2}$$
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