Question

Сократить дробь $\frac{\sqrt{-m}-2 }{m+4}$

Answer 1

$\frac{\sqrt{-m}\, -2}{m+4}=\Big [-m\geq 0\; \to \; m\leq 0\; \; \to \; \; |m|=-m\; ,\; m+4=4-|m|\; \Big ]=\\\\=\frac{\sqrt{-m}\, -2}{2^2-(\sqrt{|m|})^2}=\frac{\sqrt{-m}\, -2}{(2-\sqrt{-m})(2+\sqrt{-m})}=\frac{-(2-\sqrt{-m})}{(2+\sqrt{-m})(2-\sqrt{-m})}=-\frac{1}{2+\sqrt{-m}}$