Question

Ex 10 va rog..........

Answer 1

[tex]\it \dfrac{x}{4}=\dfrac{y}{5} = k \Leftrightarrow \begin{cases}x=4k \\\;\\ y=5k,\ \ k\in \mathbb{R} \end{cases}[/tex]

a) 

$\it \dfrac{y-x}{y+x} = \dfrac{5k-4k}{5k+4k} =\dfrac{k}{9k} =\dfrac{1}{9}$

b)

$\it \dfrac{3y+2x}{4y-x} = \dfrac{3\cdot5k+2\cdot4k}{4\cdot5k - 4k} = \dfrac{15k+8k}{20k-4k} =\dfrac{23k}{16k} = \dfrac{23}{16}\ .$