$$\frac{3x}{x-2}+\frac{5x}{x-6}=8$$
$x = \frac{8}{3} = 2\frac{2}{3} \approx 2.666666667$
$$\left(x-6\right)\times 3x+\left(x-2\right)\times 5x=8\left(x-6\right)\left(x-2\right)$$
$$\left(3x-18\right)x+\left(x-2\right)\times 5x=8\left(x-6\right)\left(x-2\right)$$
$$3x^{2}-18x+\left(x-2\right)\times 5x=8\left(x-6\right)\left(x-2\right)$$
$$3x^{2}-18x+\left(5x-10\right)x=8\left(x-6\right)\left(x-2\right)$$
$$3x^{2}-18x+5x^{2}-10x=8\left(x-6\right)\left(x-2\right)$$
$$8x^{2}-18x-10x=8\left(x-6\right)\left(x-2\right)$$
$$8x^{2}-28x=8\left(x-6\right)\left(x-2\right)$$
$$8x^{2}-28x=\left(8x-48\right)\left(x-2\right)$$
$$8x^{2}-28x=8x^{2}-64x+96$$
$$8x^{2}-28x-8x^{2}=-64x+96$$
$$-28x=-64x+96$$
$$-28x+64x=96$$
$$36x=96$$
$$x=\frac{96}{36}$$
$$x=\frac{8}{3}$$
Show Solution
Hide Solution
