Chapter 1 - Section 1.2 - Quadratic Equations - 1.2 Assess Your Understanding - Page 101: 29

$x=-\frac{3}{4}, 2$

We simplify as follows: $\frac{4(x-2)}{x-3}+\frac{3}{x}=\frac{-3}{x(x-3)}$ $\frac{4x(x-2)}{x(x-3)}+\frac{3(x-3)}{x(x-3)}=\frac{-3}{x(x-3)}$ $4x(x-2)+3(x-3)=-3$ $4x^{2}-5x-6=0$ $(4x+3)(x-2)=0$ $x=-\frac{3}{4}, 2$