Question

115. Giải phương trình: \(\dfrac{3x-1}{3x+1}=2-\dfrac{x-3}{x+3}\)

Answer 1

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

\(\Leftrightarrow\dfrac{3x-1}{3x+1}=\dfrac{2\left(x+3\right)-\left(x-3\right)}{x+3}\)

\(\Leftrightarrow\dfrac{3x-1}{3x+1}=\dfrac{2x+6-x+3}{x+3}\)

\(\Leftrightarrow\dfrac{3x-1}{3x+1}=\dfrac{x+9}{x+3}\)

\(\Leftrightarrow\left(3x-1\right)\left(x+3\right)=\left(x+9\right)\left(3x+1\right)\)

\(\Leftrightarrow3x^2+8x-3=3x^2+28x+9\)

\(\Leftrightarrow-20x=12\)

\(\Leftrightarrow x=\dfrac{-3}{5}\)

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