[tex]\displaystyle \mathtt{a) \frac{2}{x+2}= \frac{4}{x+3}\Rightarrow 2(x+3)=(x+2) \cdot 4 \Rightarrow 2x+6=4x+8 \Rightarrow }\\ \\ \mathtt{\Rightarrow 2x-4x=8-6 \Rightarrow -2x=2 \Rightarrow x=- \frac{2}{2}\Rightarrow x=-1 }\\ \\ \mathtt{b) \frac{x+2}{3}= \frac{4x}{2}\Rightarrow (x+2) \cdot 2=3 \cdot 4x \Rightarrow 2x+4=12x \Rightarrow 2x-12x=-4}\\ \\ \mathtt{\Rightarrow -10x=-4 \Rightarrow x= \frac{4}{10}\Rightarrow x= \frac{2}{5} }[/tex]
