Question

Dacă a/b = 5/3, atunci a-b/a+b = ?

Answer 1

a/b = 5/3 => a = 5b/3

(a - b)/(a + b) =

= (5b/3 - b)/(5b/3 + b)

= (2b/3)/(8b/3)

= 2/8 = 1/4

Answer 2

$Daca\ \frac{a}{b}=\frac{5}{3}, stiind\ ca\ produsul\ extremilor\ este\ egal\ cu\ produsul\ miezilor,\ 3a=5b. ->\ a=\frac{5b}{3}\\\\\frac{a-b}{a+b}=\frac{\frac{5b}{3}-b}{\frac{5b}{3}+b}\\\\Amplificam\ pe\ b\ cu\ 3\ si\ sus\ si\ jos.\\\\\frac{a-b}{a+b}=\frac{\frac{5b-3b}{3}}{\frac{5b+3b}{3}}=\frac{\frac{2b}{2}}{\frac{8b}{3}}\\\\\frac{a-b}{a+b}=\frac{2b}{3}:\frac{8b}{3}=\frac{2b}{3}*\frac{3}{8b}=\frac{2b}{8b}=\frac{1}{4}$