Question

1/x-1/x-3=4/3 solve by root of completing square method

Answer 1

$\frac{1}{x} - \frac{1}{x - 3} = \frac{4}{3} \\ \\ \frac{(x - 3) - x}{x(x - 3)} = \frac{4}{3} \\ \\ 4x(x - 3) = - 9 \\ \\ 4( {x}^{2} - 3x) = - 9 \\ \\ 4( {x}^{2} - 3x + \frac{9}{4} - \frac{9}{4} ) = - 9 \\ \\ 4( {x}^{2} - 3x + \frac{9}{4} - 9 = - 9 \\ \\ 4( {x}^{2} - 2 \times \frac{3}{2} x + {( \frac{3}{2}) }^{2} ) = 0 \\ \\ 4 {(x - \frac{3}{2} )}^{2} = 0 \\ \\ x = \frac{3}{2}$

hope it helps.