Question

Stiind ca a supra b=3 supra 7, aflati a+b supra b-a.​

Answer 1

Răspuns:

Explicație pas cu pas:

a / b = 3 / 7 ⇒    a = 3 si b = 7

( a + b ) / ( b - a ) = ( 3 + 7 ) / ( 7 - 3 ) = 10 / 4 = 5 / 2 = 2,5

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sau:   a / b = 3 / 7 ⇒   3 b = 7 a ⇒   b = 7 a / 3

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

= ( a + 7 a / 3 ) / ( 7 a / 3 - a ) =

= ( 3 a / 3 + 7 a / 3 ) / ( 7 a / 3 - 3 a / 3 ) =

= ( 10 a / 3 ) : ( 4 a / 3 ) =

= ( 10 a / 3 ) × ( 3 / 4 a )  → se reduce 3 cu 3;  a cu a; 10 cu 4 se simplifica cu 2

= 10 / 4 =

= 5 / 2 = 2 intregi si 1 / 2 = 2,5

Answer 2

$\it \dfrac{a}{b}=\dfrac{3}{7} \Rightarrow \dfrac{a}{3}=\dfrac{b}{7}=k \Rightarrow \begin{cases}\it a=3k\\ \\ b=7k\end{cases},\ \ k\in\mathbb{Q}\\ \\ \\ \dfrac{a+b}{b-a}=\dfrac{3k+7k}{7k-3k}=\dfrac{10k}{4k}=\dfrac{\ \ 10^{(2}}{4}=\dfrac{5}{2}=2,5$