[tex] \displaystyle\\
7d)
\frac{x}{2}=\frac{y}{9}=>\frac{x}{y}=\frac{2}{9}\\\\
\frac{10x-2y}{5x+y}~\text{Simplificam fortat cu y.}\\\\
\frac{10x-2y}{5x+y}=\frac{10\cdot\dfrac{x}{y}-2\cdot\dfrac{y}{y}}{5\cdot\dfrac{x}{y}+\dfrac{y}{y}}=\frac{10\cdot\dfrac{x}{y}-2}{5\cdot\dfrac{x}{y}+1}=\frac{10\cdot\dfrac{2}{9}-2}{5\cdot\dfrac{2}{9}+1}=\\\\\\
=\frac{\dfrac{20}{9}-2}{\dfrac{10}{9}+1}=\frac{\dfrac{20-2\cdot9}{9}}{\dfrac{10+9}{9}}=\frac{\dfrac{2}{9}}{\dfrac{19}{9}}=\frac{2}{9}\cdot\frac{9}{19}= \boxed{\frac{2}{19}} [/tex]
8a)
Fractia o simplificam fortat cu y.
[tex] \displaystyle\\
\frac{x+y}{2x+y}=\frac{4}{5}\\\\\\
\frac{\dfrac{x}{y}+\dfrac{y}{y}}{2\cdot\dfrac{x}{y}+\dfrac{y}{y}}=\frac{4}{5}\\\\\\
\frac{\dfrac{x}{y}+1}{2\cdot\dfrac{x}{y}+1}=\frac{4}{5}\\\\\\
5\Big(\frac{x}{y}+1\Big)=4\Big(2\cdot\frac{x}{y}+1\Big)\\\\
5\cdot\frac{x}{y}+5=4\cdot2\cdot\frac{x}{y}+4\\\\
8\cdot\frac{x}{y} - 5\cdot\frac{x}{y} =5-4\\\\
3\cdot\frac{x}{y}=1\\\\
\boxed{\frac{x}{y}=\frac{1}{3}} [/tex]
8b)
Fractia o simplificam fortat cu y.
[tex] \displaystyle\\
\frac{3x+4y}{2x+y}=\frac{7}{3}\\\\\\
\frac{3\cdot\dfrac{x}{y}+4\cdot\dfrac{y}{y}}{2\cdot\dfrac{x}{y}+\dfrac{y}{y}}=\frac{7}{3}\\\\\\
\frac{3\cdot\dfrac{x}{y}+4}{2\cdot\dfrac{x}{y}+1}=\frac{7}{3}\\\\\\
7\Big(2\cdot\frac{x}{y}+1\Big)=3\Big(3\cdot\frac{x}{y}+4\Big)\\\\
7\cdot2\cdot\frac{x}{y}+7=3\cdot3\cdot\frac{x}{y}+12\\\\
7\cdot2\cdot\frac{x}{y}+7=3\cdot3\cdot\frac{x}{y}+12\\\\
14\cdot\frac{x}{y}-9\cdot\frac{x}{y}=12-7\\\\
5\cdot\frac{x}{y}=5\\\\
\frac{x}{y}=\frac{5}{5}=\boxed{1} [/tex]
