Question

solve for x:4/x-3=5/2x+3,x≠0,-3/2​

Answer 1

SOLUTION

$= > \frac{4}{x} - 3 = \frac{5}{2x + 3} \\ = > \frac{4 - 3x}{x} = \frac{5}{2x + 3} \\ = > (4 - 3x)(2x + 3) = 5x \\ = > 8x + 12 - {6x}^{2} - 9x = 5x \\ = > {6x}^{2} + 6x - 12 = 0 \\ = > {x}^{2} + x - 2 = 0 \\ = > {x}^{2} + x + \frac{1}{4} - \frac{1}{4} - 2 = 0 \\ = > ( {x}^{2} + x + \frac{1}{4} ) - \frac{9}{4} = 0 \\ = > (x + \frac{1}{2} ) {}^{2} - ( \frac{3}{2} ) {}^{2} = 0 \\ = > (x + \frac{1}{2} ) {}^{2} = ( \frac{3}{2} ) {}^{2} \\ = > (x + \frac{1}{2} ) = + - \frac{3}{2} \\ = > x = \frac{3}{2} - \frac{1}{2} \: or \: x = - \frac{3}{2} - \frac{1}{2} \\ = > x = \frac{2}{2} \: \: or \: \: \: x = - \frac{4}{2} \\ \\ = > x = 1 \: \: or \: \: \: x = - 2$

hope it helps ☺️