$$\frac{3x}{x+2}+\frac{4x}{x-4}=7$$
$x = -\frac{28}{5} = -5\frac{3}{5} = -5.6$
$$\left(x-4\right)\times 3x+\left(x+2\right)\times 4x=7\left(x-4\right)\left(x+2\right)$$
$$\left(3x-12\right)x+\left(x+2\right)\times 4x=7\left(x-4\right)\left(x+2\right)$$
$$3x^{2}-12x+\left(x+2\right)\times 4x=7\left(x-4\right)\left(x+2\right)$$
$$3x^{2}-12x+\left(4x+8\right)x=7\left(x-4\right)\left(x+2\right)$$
$$3x^{2}-12x+4x^{2}+8x=7\left(x-4\right)\left(x+2\right)$$
$$7x^{2}-12x+8x=7\left(x-4\right)\left(x+2\right)$$
$$7x^{2}-4x=7\left(x-4\right)\left(x+2\right)$$
$$7x^{2}-4x=\left(7x-28\right)\left(x+2\right)$$
$$7x^{2}-4x=7x^{2}-14x-56$$
$$7x^{2}-4x-7x^{2}=-14x-56$$
$$-4x=-14x-56$$
$$-4x+14x=-56$$
$$10x=-56$$
$$x=\frac{-56}{10}$$
$$x=-\frac{28}{5}$$
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