Elementary Geometry for College Students (6th Edition)

$x = -\frac{9}{5}, 4$
1. Expand and simplify the equation $\frac{x(x+5)}{4x+4} = \frac{9}{5}$ $\frac{(x^{2}+5x)}{4x+4} = \frac{9}{5}$ $5(x^{2} + 5x) = 9(4x+4)$ $5x^{2} + 25x = 36x+36$ $5x^{2} + 25x -36x -36 = 0$ $5x^{2} - 11x -36 = 0$ $5x^{2} - 20x +9x - 36 = 0$ $5x(x-4) + 9(x-4) = 0$ $(5x+9)(x-4) = 0$ 2. Separate the components of the last equation into $(5x+9) = 0$ and $(x-4) = 0$ $(5x+9) = 0$ $5x = -9$ $x = -\frac{9}{5}$ $(x-4) = 0$ $x = 4$ Therefore, $x = -\frac{9}{5}, 4$