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