Question

Dacă
$\frac{x}{y} = \frac{4}{5}$
Atunci
$\frac{5x - 3y}{x + y} = ...$
Va rog ajutatima dau coroniță

Answer 1

aplic propietatile de la proportii (proportii derivate)

x/y=4/5 echivalent cu

x/x+y=4/5+4

x/x+y=4/9

deci x+y= 9x/4

dar din x/y=4/5 rezulta ca 5x=4y pe care il inlocuim in urmatoarea:

deci 5x-3y/x+y = 4y-3y/x+y = y/x+y=y/(9x/4)=y/x*4/9=5/4*4/9=5/9

Answer 2

x/y = 4/5
x = 4y/5
(5x - 3y)/(x + y) =
(5 * 4y/5 - 3y)/(4y/5 + ⁵⁾y) =
(4y - 3y)/(4y/5 + 5y/5) =
y/(9y/5) = 
y * 5/9y =
5/9