Question

daca x/y = 3/5, atunci x+2y/2x+y este:

Answer 1

Răspuns:

13/11

Explicație pas cu pas:

vom imparti numaratorul si numitorul fractiei (x+2y)/(2x+y) la y,

$\frac{x+2y}{2x+y}=\frac{x+2y}{y} :\frac{2x+y}{y}=(\frac{x}{y}+\frac{2y}{y}):(\frac{2x}{y}+\frac{y}{y})=(\frac{3}{5}+2):(\frac{6}{5}+1)=\frac{13}{5}:\frac{11}{5}=\frac{13}{5}*\frac{5}{11}=\frac{13}{11}$

Answer 2

$\dfrac{x}{y} = \dfrac{3}{5}\\ \\ \\\dfrac{x+2y}{2x+y} = \dfrac{x+2y}{2x+y}\cdot \dfrac{\dfrac{1}{y}}{\dfrac{1}{y}} = \dfrac{\dfrac{x}{y}+2}{\dfrac{2x}{y}+1} = \\ \\ = \dfrac{\dfrac{3}{5}+2}{2\cdot \dfrac{3}{5}+1}\cdot \dfrac{5}{5}= \dfrac{3+2\cdot 5}{2\cdot 3+5} = \boxed{\dfrac{13}{11}}$