$$\frac{x+5}{6}-\frac{x+1}{9}=\frac{x+3}{4}$$
$x=-\frac{1}{7}\approx -0.142857143$
$$6\left(x+5\right)-4\left(x+1\right)=9\left(x+3\right)$$
$$6x+30-4\left(x+1\right)=9\left(x+3\right)$$
$$6x+30-4x-4=9\left(x+3\right)$$
$$2x+30-4=9\left(x+3\right)$$
$$2x+26=9\left(x+3\right)$$
$$2x+26=9x+27$$
$$2x+26-9x=27$$
$$-7x+26=27$$
$$-7x=27-26$$
$$-7x=1$$
$$x=\frac{1}{-7}$$
$$x=-\frac{1}{7}$$
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