Chapter 7 - Algebraic Fractions - 7.5 - Fractional Equations and Problem Solving - Problem Set 7.5 - Page 306: 35

$x = -6$

1. Multiply by $x-2$ on both sides of the equation to obtain: $-1 - \frac{5}{x-2} = \frac{3}{x-2}$ $-1(x-2) - 5 = \frac{3(x-2)}{x-2}$ 2. Cancel out $x-2$ in the fraction to simplify: $-1(x-2) - 5 = 3$ 3. Expand and solve for $x$: $-x + 2 - 5 = 3$ $-x + 2 - 5 - 3 = 0$ $-x + 2 -8 = 0$ $-x - 6 = 0$ $-x -6 = 0$ $-x = 6$ $x = -6$