Question

solve for x : 2(2x-1/x+3)-3(x+3/2x-1)=5

Answer 1

$\frac{2(2x - 1)}{(x + 3)} - \frac{3(x + 3)}{(2x - 1))} = 5 \\ \\ = > \frac{2 {(2x - 1)}^{2} - 3 {(x + 3)}^{2} }{(x + 3)(2x - 1)} = 5 \\ \\ = > \frac{2(4 {x}^{2} - 4x + 1) - 3( {x}^{2} + 6x + 9) }{2 {x}^{2} - x + 6x - 3 } = 5 \\ \\ = > 8 {x}^{2} - 8x + 2 - 3 {x}^{2} - 18x - 27 = 10 {x}^{2} + 25x - 15 \\ \\ = > 10 {x}^{2} - 5 {x}^{2} + 25x + 26x - 15 + 25 = 0 \\ \\ = > 5 {x}^{2} + 51x + 10 = 0 \\ \\ = > 5 {x}^{2} + 50x + x + 10 = 0 \\ \\ = > 5x(x + 10) + 1(x + 10) = 0 \\ \\ = > (5x + 1)(x + 10) = 0$

Required values of x : -1/5 and -10

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