## College Algebra (10th Edition)

$\frac{2x}{x+3}=\frac{-6}{x+3}-2$ The LCD is (x-3) where $x\ne-3$ $(x+3)\frac{2x}{x+3}=(\frac{-6}{x+3}-2)(x+3)$ Multiply both sides by x+3. $(x+3)\frac{2x}{x+3}=(x+3)\frac{-6}{x+3}-2(x+3)$ Distribute, divide out common factors. $2x=-6-2(x+3)$ $2x=-6-2x-6$ Distribute, combine like terms. $2x+2x=-12-2x+2x$ Add 2x to both sides $4x=-12$ $\frac{4}{4}x=\frac{12}{4}$ Divide both sides by 4. $x=-3$ The equation has no solution because $x=-3$ creates a divide by zero error.