Question

Se ştie că [tex] \frac{x}{y} = \frac{2}{7} . Calculati:
A) \frac{2x}{3y} ;
B) \frac{x+y}{y};
C) \frac{x}{y-x} ;
D) \frac{2x+3y}{5y} [/tex]

Answer 1

$\frac{x}{y}=\frac{2}{7} \ \ \Rightarrow x=\frac{2y}{7}; \ \ y=\frac{7x}{2}; \\ \bold{a)} \ \frac{2x}{3y}=\frac{3\cdot \frac{2y}{7}}{3y}=\frac{6y}{7}:\frac{3y}{1}=\frac{6y}{7} \cdot \frac{1}{3y}=\frac{6y}{21y}=\boxed{\frac{2}{7}};\\ \bold{b)} \ \frac{x+y}{y}=\frac{\frac{2y}{7}+y}{y}=\frac{\frac{2y}{7}+\frac{7y}{7}}{y}=\frac{9y}{7}\cdot\frac{1}{y}=\frac{9y}{7y}=\boxed{\frac{9}{7}};$
$\bold{c)}\ \frac{x}{y-x}=\frac{x}{\frac{7x}{2}-x}=\frac{x}{1}:(\frac{7x}{2}-\frac{2x}{2})=\frac{x}{1}\cdot \frac{2}{5x}=\frac{2x}{5x}=\boxed{\frac{2}{5}};\\ \bold{d)} \ \frac{2x+3y}{5y}=\frac{2 \cdot \frac{2y}{7}+3y}{5y}=\frac{\frac{4y}{7}+\frac{21y}{7}}{5y}=\frac{25y}{7}:\frac{5y}{1}=\frac{25y}{7}\cdot\frac{1}{5y}=\frac{25y}{35y}=\boxed{\frac{5}{7}}.$