# How do you solve (2x-3)/(x+3)=(3x)/(x+4)?

$x = - 2 + 2.828 i , x = - 2 - 2.828 i$
$\frac{2 x - 3}{x + 3} = \frac{3 x}{x + 4} \mathmr{and} \left(2 x - 3\right) \left(x + 4\right) = 3 x \left(x + 3\right) \mathmr{and} 2 {x}^{2} + 5 x - 12 = 3 {x}^{2} + 9 x \mathmr{and} {x}^{2} + 4 x + 12 = 0 \mathmr{and} {\left(x + 2\right)}^{2} - 4 + 12 = 0 \mathmr{and} {\left(x + 2\right)}^{2} = - 8 \mathmr{and} \left(x + 2\right) = \pm \sqrt{- 8} \mathmr{and} \left(x + 2\right) = 2 \sqrt{2} i \mathmr{and} x = - 2 + 2 \sqrt{2} i \mathmr{and} x = - 2 - 2 \sqrt{2} i \mathmr{and} x = - 2 + 2.828 i , x = - 2 - 2.828 i$[Ans]