$$\frac{x+3}{4}+\frac{x+1}{9}=\frac{x+5}{6}$$
$x=-\frac{1}{7}\approx -0.142857143$
$$9\left(x+3\right)+4\left(x+1\right)=6\left(x+5\right)$$
$$9x+27+4\left(x+1\right)=6\left(x+5\right)$$
$$9x+27+4x+4=6\left(x+5\right)$$
$$13x+27+4=6\left(x+5\right)$$
$$13x+31=6\left(x+5\right)$$
$$13x+31=6x+30$$
$$13x+31-6x=30$$
$$7x+31=30$$
$$7x=30-31$$
$$7x=-1$$
$$x=\frac{-1}{7}$$
$$x=-\frac{1}{7}$$
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