Question

solve for x : ((x+3)/(x-2)) - (1-x)/x = 17/4

Answer 1

$\underline{\Large\mathbf{Question}}$

$\frac{(x + 3)}{(x - 2)} - \frac{(1 - x)}{x} = \frac{17}{4}$

$\underline{\underline{\huge\mathfrak{Solution}}}$

$\underline{\mathbf{Taking \: L.C.M \: we \: get}}$

$\frac{x(x + 3) - (x - 2)(1 - x)}{(x - 2)(x)} = \frac{17}{4} \\ \\ \frac{ {x}^{2} + 3x - (x - {x}^{2} - 2 + 2x)}{ {x}^{2} - 2x } = \frac{17}{4} \\ \\ \frac{ {x}^{2} + 3x - x + {x}^{2} + 2 - 2x}{ {x}^{2} - 2x} = \frac{17}{4} \\ \\ \frac{ {x}^{2} + {x}^{2} + 3x - 2x + 2 }{ {x}^{2} - 2x} = \frac{17}{4} \\ \\ \frac{2 {x}^{2} + x + 2}{ {x}^{2} - 2x} = \frac{17}{4}$

$\underline{\mathbf{On \: Cross \: Multiplication \: we \: get,}}$

$4(2 {x}^{2} + x + 2) = 17( {x}^{2} - 2x) \\ \\ 8 {x}^{2} + 4x + 8 = 17 {x}^{2} - 34x \\ \\ 8 {x}^{2} - 17 {x}^{2} + 4x + 34x + 8= 0 \\ \\ - 9 {x}^{2} + 38x + 8 = 0 \\ \\ 9 {x}^{2} - 38x + 8 = 0 \\ \\ 9 {x}^{2} - 36x - 2x + 8 = 0\\ \\ 9x(x - 4) - 2(x - 4) = 0 \\ \\ (9x - 2)(x - 4) = 0 \\ \\ 9x - 2 = 0 \: \: and \: \: x - 4 = 0 \\ \\ \bf x = \frac{2}{9} \: \: and \: \: x = 4$