Question

Tìm tỉ số

1) \(\frac{x}{y}\) biết\(\frac{2x-y}{x+y}=\frac{2}{3}\)

2)\(\frac{a+b}{b+c}\) biết \(\frac{b}{a}=2;\frac{c}{b}=3\)

Answer 1

1) \(\frac{2x-y}{x+y}=\frac{2}{3}\)

\(\Leftrightarrow\left(2x-y\right).3=2\left(x+y\right)\)

\(\Leftrightarrow6x-3y=2x+2y\)

\(\Leftrightarrow6x-2x=2y+3y\)

\(\Rightarrow4x=5y\)

\(\Rightarrow\frac{x}{y}=\frac{5}{4}\)

2) \(\begin{cases}\frac{b}{a}=2\\\frac{c}{b}=3\end{cases}\) \(\Rightarrow\begin{cases}b=2a\\c=3b\end{cases}\)

Khi đó: \(\frac{a+b}{b+c}=\frac{a+2a}{2a+3}\)

\(=\frac{a+2a}{2a+3.2a}\)

\(=\frac{3a}{8a}=\frac{3}{8}\)

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