<s>[INST] Simplifying $\frac{a^x}{a^x+\sqrt{a}} + \frac{a^{1-x}}{a^{1-x}+\sqrt{a}}$ While solving a problem related to functions, I came across the following algebraic expression: 
$$\frac{a^x}{a^x+\sqrt{a}} + \frac{a^{1-x}}{a^{1-x}+\sqrt{a}}$$
Although I tried, I couldn't find an easy way to simplify it.

Can anyone simplify the stated equation in the easiest way so that anyone can understand it?

 [/INST] $\ {a ^ x \over a^x + \sqrt a} + {a ^ {1-x} \over 
    a ^ {1-x} + \sqrt a}$
Well, often it's a good idea to put over common denominator:
$\frac {a^x(a^{1-x} + \sqrt a) + a^{1-x}(a^x+\sqrt a)}{(a^x + \sqrt a)(a^{1-x} + \sqrt a)} =$
$\frac {(a^{x + 1-x} + a^x\sqrt a) + (a^{1-x+x} + a^{1-x}\sqrt a)}{a^{x+1-z} + a^x\sqrt a + a^{1-x}\sqrt a + a}=$
$\frac {2a^1 + (a^x + a^{1-x})\sqrt a}{2a+(a^x + a^{1-x})\sqrt a} = 1$.
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