$$\frac{3}{x-2}+\frac{x+3}{4-x^{2}}=\frac{6}{x+2}$$
$x = \frac{15}{4} = 3\frac{3}{4} = 3.75$
$$\left(x+2\right)\times 3-\left(x+3\right)=\left(x-2\right)\times 6$$
$$3x+6-\left(x+3\right)=\left(x-2\right)\times 6$$
$$3x+6-x-3=\left(x-2\right)\times 6$$
$$2x+6-3=\left(x-2\right)\times 6$$
$$2x+3=\left(x-2\right)\times 6$$
$$2x+3=6x-12$$
$$2x+3-6x=-12$$
$$-4x+3=-12$$
$$-4x=-12-3$$
$$-4x=-15$$
$$x=\frac{-15}{-4}$$
$$x=\frac{15}{4}$$
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