Solve for x: $\frac{1}{x+1} +\frac{3}{5x+1} = \frac{5}{x+4}, x\ne-1, -\frac{1}{5}, -4$

Solve for x:

$$ \frac{1}{x+1} +\frac{3}{5x+1} = \frac{5}{x+4}, x\ne-1, -\frac{1}{5}, -4 $$

[(5x + 1) + (x + 1)3](x + 4) = 5(x + 1) (5x + 1)

(8x + 4)(x + 4) = 5(5x² + 6x + 1)

17x² - 6x - 11 = 0

(17x + 11)(x - 1) = 0

$$ x = \frac{-11}{17}, x = 1 $$