1. **State the problem:** Solve for $x$ in the equation $$\frac{0.853}{0.972} = \frac{x}{0.0750} \times \frac{0.642}{0.972} + \frac{x}{0.188}.$$\n\n2. **Rewrite the equation clearly:** $$\frac{0.853}{0.972} = x \times \frac{0.642}{0.972 \times 0.0750} + \frac{x}{0.188}.$$\n\n3. **Calculate the constants:**\n$$\frac{0.853}{0.972} \approx 0.87716,$$\n$$\frac{0.642}{0.972 \times 0.0750} = \frac{0.642}{0.0729} \approx 8.80247.$$\n\n4. **Substitute back:** $$0.87716 = 8.80247x + \frac{x}{0.188}.$$\n\n5. **Express the second term with a common denominator:** $$\frac{x}{0.188} \approx 5.31915x.$$\n\n6. **Combine like terms:** $$0.87716 = 8.80247x + 5.31915x = (8.80247 + 5.31915)x = 14.12162x.$$\n\n7. **Solve for $x$:** $$x = \frac{0.87716}{14.12162} \approx 0.06207.$$\n\n**Final answer:** $$x \approx 0.0621.$$