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Solving a Quadratic Equation by Factorization Method

Solve: 22x-1...

Question

Solve: $2 (\frac{2 x - 1}{x + 3}) - 3 (\frac{x + 3}{2 x - 1}) = ?$

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Solution

$2 (\frac{2 x - 1}{x + 3}) - 3 (\frac{x + 3}{2 x - 1}) = 5 \Rightarrow 2 (2 x - 1) (2 x - 1) - 3 (x + 3) (x + 3) = 5 (x + 3) (2 x - 1) \Rightarrow 5 x^{2} + 51 x + 10 = 0 \Rightarrow 5 x^{2} + 50 x + x + 10 = 0 \Rightarrow 5 x (x + 10) + 1 (x + 10) = 0 \Rightarrow (x + 10) (5 x + 1) = 0 \Rightarrow x = - 100 r - \frac{1}{5}$

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