I DO NOT NEED HELP.(<- for Melody.....) and fun simplification questions!

Very impressive Max :D

Thanks Max :))

I would like you to share your answers to these questions.

I will go first :)

1) $\dfrac{x^{-1}+y^{-1}}{x+y}\\ =\dfrac{(x^{-1}+y^{-1})(xy)}{(x+y)(xy)}\\ =\dfrac{y + x}{(x+y)(xy)}\\ = \dfrac{1}{xy}$

2)$\dfrac{x^{-1}-y^{-1}}{x-y}\\ =\dfrac{(x^{-1}-y^{-1})(xy)}{(x-y)(xy)}\\ = \dfrac{-(x-y)}{(x-y)(xy)}\\ =-\dfrac{1}{xy}$

3)$\dfrac{x^{-2}+y^{-2}}{x+y}\\ =\dfrac{\frac{1}{x^2}+\frac{1}{y^2}}{x+y}\\ = \dfrac{\frac{x^2+y^2}{(xy)^2}}{x+y}\\ =\dfrac{x^2+y^2}{(xy)^2(x+y)}$

4)$\dfrac{x^{-2}-y^{-2}}{x-y}\\ =\dfrac{(x^{-1}+y^{-1})(x^{-1}-y^{-1})}{x-y}\\ =\dfrac{x^{-1}-y^{-1}}{x-y}(x^{-1}+y^{-1})\\ =-\dfrac{x^{-1}+y^{-1}}{xy}$

The last step of 4) is from 2)!!

Why are you guys so good at math :( LOL