<s>[INST] Subtraction of fractional exponents with different bases I wanna know if $$\left[(x^2+h)^3-(x+h)\right]^{1/2}-[x^3-x]^{1/2}=\left[(x+h)^3-(x+h)-x^3+x\right]^{1/2}.$$
 [/INST] Does $a^2 - b^2 = (a-b)^2\;$?
No,  Because $$(a-b)^2 = a^2 -2ab +b^2 \neq a^2 - b^2$$
Alternatively $$a^{1/2} - b^{1/2} = \sqrt a -\sqrt b \neq \sqrt{a-b}$$
Simply take $a = 4, b = 9$.  Then we have $2 - 3 = -1$. Whereas $\sqrt{2-3}$ is undefined in the reals, and which will never be equal to a negative real number.
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