Question

Daca a supra b =2 supra 5 atunci b+a supra b-a este egal cu .....

Answer 1

$\frac{a}{b}=\frac{2}{5}$
$\frac{a}{2}=\frac{b}{5}$
$a=2k,~b=5k$
$\frac{b+a}{b-a}=\frac{5k+2k}{5k-2k}$
$=\frac{7k}{3k}=\frac{7}{3}$

Answer 2

$\dfrac{a}{b} = \dfrac{2}{5} \Rightarrow a = b\cdot \dfrac{2}{5} \\ \\ \\ \dfrac{b+a}{b-a} = \dfrac{b+b\cdot \dfrac{2}{5}}{b-b\cdot \dfrac{2}{5}} = \dfrac{\not{b}\cdot \Big(1+\dfrac{2}{5}\Big)}{\not{b}\cdot \Big(1-\dfrac{2}{5}\Big)} = \dfrac{^{\big{5)}}1+\dfrac{2}{5}}{^{\big{5)}}1-\dfrac{2}{5}} = \dfrac{\dfrac{5+2}{5}}{\dfrac{5-2}{5}} = \dfrac{5+2}{\not5}\cdot \dfrac{\not5}{5-2}= \\ \\ =\dfrac{5+2}{5-2} = \dfrac{7}{3}$