Answer
$x = -\frac{9}{5}, 4$
Work Step by Step
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, $x = -\frac{9}{5}, 4$
