Question
Solve: $\frac{9\text{x}-7}{3\text{x}+5}=\frac{3\text{x}-4}{\text{x}+6}$
✓
Answer
$\frac{9\text{x}-7}{3\text{x}+5}=\frac{3\text{x}-4}{\text{x}+6}$ $\Rightarrow (\text{x}+6) (9\text{x}-7) = (3\text{x}+5) (3\text{x}-4)$ $\Rightarrow9\text{x}^2 - 7\text{x} + 54\text{x} - 42 = 9\text{x}^2 - 12\text{x} + 15\text{x} - 20$ $\Rightarrow9\text{x}^2 + 47\text{x} - 42 = 9\text{x}^2 + 3\text{x} - 20$ $\Rightarrow 9\text{x}^2 - 9\text{x}^2 + 47\text{x} - 3\text{x} = -20 + 42$ $\Rightarrow44\text{x} = 22$ $\Rightarrow \text{x} = \frac{22}{44}= \frac{1}{2}$ $\therefore\text{x}=\frac{1}{2}$
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