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True or False.

$\dfrac{1+\dfrac{1}{x}}{1-\dfrac{1}{x^2}} = \left(1+\dfrac{1}{x}\right) \div \left(1-\dfrac{1}{x^2}\right)$

$\dfrac{1+\dfrac{1}{x}}{1-\dfrac{1}{x^2}} = \dfrac{x+1}{x^2+1}$

$\left(a^{-1}+b^{-1}\right)^{-2} = a^{-2} + b^{-2}$

$\dfrac{\dfrac{1}{a} - \dfrac{1}{b}}{\dfrac{1}{a} + \dfrac{1}{b}} = \dfrac{\dfrac{1}{a-b}}{\dfrac{1}{a+b}}$

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