## Algebra 1

$x=9$
$\frac{x-6}{x+3}+\frac{2x}{x-3}=\frac{4x+3}{x+3}$ $\frac{x-6}{x+3}*(x-3)/(x-3)+\frac{2x}{x-3}*(x+3)/(x+3)=\frac{4x+3}{x+3}*(x-3)/(x-3)$ $\frac{(x-6)(x-3)}{(x+3)(x-3)}+\frac{(2x)(x+3)}{(x-3)(x+3)}=\frac{(4x+3)(x-3)}{(x+3)(x-3)}$ $((x-6)(x-3)+(2x)(x+3))/{(x-3)(x+3)}=\frac{(4x+3)(x-3)}{(x+3)(x-3)}$ $((x-6)(x-3)+(2x)(x+3))=(4x+3)*(x-3))$ $x^2-9x+18 +2x^2+6x = 4x^2-12x+3x-9$ $3x^2-3x+18 = 4x^2-9x-9$ $3x^2-3x+18-3x^2+3x-18 = 4x^2-9x-9-3x^2+3x-18$ $0 = x^2-6x-27$ $(x-9)(x+6)=0$ $x-9=0$ $x=9$ $x+6=0$ $x=-6$ $x=9$ $\frac{x-6}{x+3}+\frac{2x}{x-3}=\frac{4x+3}{x+3}$ $\frac{9-6}{9+3}+\frac{2*9}{9-3}=\frac{4*9+3}{9+3}$ $\frac{3}{12}+\frac{18}{6}=\frac{39}{12}$ $.25 + 3 = 3.25$ $x=-6$ $\frac{x-6}{x+3}+\frac{2x}{x-3}=\frac{4x+3}{x+3}$ $\frac{-6-6}{-6+3}+\frac{2*-6}{-6-3}=\frac{4*-6+3}{-6+3}$ $\frac{-12}{-3}+\frac{-12}{-9}=\frac{-21}{-9}$ $4 +4/3 = 7/3$ (not true, so this answer is invalid)