Question

$\huge\tt\bold{2 (\frac{2x - 1}{x + 3} ) - 3 ( \frac{x + 3}{2x - 1} ) = 5}$ find value of x answer with step by step

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Answer 1

$\huge\tt\red{\bold{\underline{\underline{❥Question᎓}}}}$$\huge\tt\bold{2 (\frac{2x - 1}{x + 3} ) - 3 ( \frac{x + 3}{2x - 1} ) = 5}$

$\huge\mathcal{Answer}$

GIVEN:-

$\bold{\boxed{\boxed{\green{2 (\frac{2x - 1}{x + 3} ) - 3 ( \frac{x + 3}{2x - 1} ) = 5}}}}$

$⟹\bold{2 (\frac{2x - 1}{x + 3} ) - 3( \frac{x + 3}{2x - 1} ) = 5}$

$⟹\bold{\frac{2 {(2x - 1) }^{2} - 3 {(x + 3)}^{2} }{(x + 3)(2x - 1)} = 5}$

$⟹\bold{2(4 {x}^{2} - 4x + 1) - 3( {x}^{2} + 6x + 9)}$

$\bold{= 5(2 {x}^{2} + 6x - x - 3)}$

$⟹\bold{8 {x}^{2} - 8x + 2 - 3 {x}^{2} - 18x - 27}$

$\bold{ = 10 {x}^{2} + 30x - 5x - 15}$

$⟹\bold{5 {x}^{2} + 51x + 10 = 0}$

$⟹\bold{5 {x}^{2} + 50x + x + 10 = 0}$

$⟹\bold{5x(x + 10) + 1(x + 10) = 0}$

$⟹\bold{(x + 10)(5x + 1) = 0}$

$⟹\bold{x + 10 = 0}$

$⟹\bold{5x + 1 = 0}$

$\bold{\boxed{\red{x = - 10}}}$

$\bold{\boxed{x = - \frac{1}{5}}}$

$\bold{\boxed{∴The \:solutions\: are \:-20\: and\: -1/5}}$

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