1. **State the problem:** Simplify the expression $$\frac{140+35x}{150+30x}$$ and check if it can be written as $$\frac{14+7x}{15+6x}$$. 2. **Identify common factors:** Look for common factors in numerator and denominator. 3. **Factor numerator:** $$140+35x = 35(4+x)$$. 4. **Factor denominator:** $$150+30x = 30(5+x)$$. 5. **Simplify the fraction:** $$\frac{140+35x}{150+30x} = \frac{35(4+x)}{30(5+x)} = \frac{7 \cdot 5 (4+x)}{6 \cdot 5 (5+x)} = \frac{7(4+x)}{6(5+x)}$$. 6. **Compare with proposed form:** $$\frac{14+7x}{15+6x} = \frac{7(2+x)}{3(5+2x)}$$. 7. **Conclusion:** The simplified form $$\frac{7(4+x)}{6(5+x)}$$ is not equal to $$\frac{7(2+x)}{3(5+2x)}$$, so the expression cannot be simplified to $$\frac{14+7x}{15+6x}$$. **Final answer:** The simplified form is $$\frac{7(4+x)}{6(5+x)}$$, not $$\frac{14+7x}{15+6x}$$.