.............................
![class=](https://ro-static.z-dn.net/files/ddc/b1adf35c0225bc0683b1c5f889b78a24.jpg)
Răspuns:
Explicație pas cu pas:
5(5a + 2b) = 4(7a + 2b)
25a + 10b = 28a + 8b
28a - 25a = 10b - 8b
3a = 2b
a = 2b/3
2a - b = 4b/3 - 3b/3 = b/3
a + b = 2b/3 + 3b/3 = 5b/3
(2a - b)/(a + b) = b/3 : 5b/3 = b/3*3/5b = 3b/15b = 1/5
[tex]\it \dfrac{5a+2b}{7a+2b}=\dfrac{4}{5} \Rightarrow \dfrac{5a+2b}{7a+2b-5a-2b}=\dfrac{4}{5-4} \Rightarrow \dfrac{5a+2b}{2a}=4 \Rightarrow \\ \\ \\ \Rightarrow 5a+2b=8a|_{-5a} \Rightarrow 2b=3a|_{:2} \Rightarrow b=1,5a\ \ \ \ \ \ (*)\\ \\ \\ \dfrac{2a-b}{a+b}\ \stackrel{(*)}{=}\ \dfrac{2a-1,5a}{a+1,5a}=\dfrac{0,5a}{2,5a}= \dfrac{^{2)}0,5}{\ 2,5}=\dfrac{1}{5}[/tex]