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[tex]\sf(a^{-2}-b^{-2})\cdot(a^{-1}-b^{-1})^{-1}\\\sf\bigg(\dfrac{1}{a^2}-\dfrac{1}{b^2}\bigg)\cdot\bigg(\dfrac{1}{a}-\dfrac{1}{b}\bigg)^{-1}\\\sf\bigg(\dfrac{b^2-a^2}{a^2\cdot b^2}\bigg)\cdot\bigg(\dfrac{b-a}{a\cdot b}\bigg)^{-1}\\\sf\bigg(\dfrac{\diagup\!\!\!\!\!(b-\diagup\!\!\!\!\!a)\cdot(b+a)}{a^2\cdot b^2}\bigg)\cdot\bigg(\dfrac{ab}{\diagup\!\!\!\!\!\!(b-\diagup\!\!\!\!\!a)}\bigg)\\\sf\dfrac{\diagup\!\!\!\!\!ab\cdot(b+a)}{\diagup\!\!\!\!\!\!ab\cdot ab}[/tex]
[tex]\huge\boxed{\boxed{\boxed{\boxed{\sf\dfrac{a+b}{ab}}}}}\blue{\checkmark}[/tex]
