$$\frac{5x-3}{7}-+\frac{9x-2}{5}=\frac{x+2}{3}$$
$x=-\frac{73}{149}\approx -0.489932886$
$$15\left(5x-3\right)-21\left(9x-2\right)=35\left(x+2\right)$$
$$75x-45-21\left(9x-2\right)=35\left(x+2\right)$$
$$75x-45-189x+42=35\left(x+2\right)$$
$$-114x-45+42=35\left(x+2\right)$$
$$-114x-3=35\left(x+2\right)$$
$$-114x-3=35x+70$$
$$-114x-3-35x=70$$
$$-149x-3=70$$
$$-149x=70+3$$
$$-149x=73$$
$$x=\frac{73}{-149}$$
$$x=-\frac{73}{149}$$
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