1. Problem: Simplify the expression $$\frac{x^2 - y^2}{x + y}$$. 2. Recognize that the numerator is a difference of squares: $$x^2 - y^2 = (x - y)(x + y)$$. 3. Substitute back into the fraction: $$\frac{(x - y)(x + y)}{x + y}$$. 4. Cancel the common factor $$x + y$$ (assuming $$x + y \neq 0$$): $$x - y$$. Final answer: $$x - y$$. 5. Problem: Interpret the given values $$75.7\; m/s$$ and $$1000\; m^2 s^{-3}$$. 6. These appear to be data or physical quantities, no direct computation requested. 7. Problem: The same as problem 1; simplified result is $$x - y$$. 8. Problem: Simplify the expression $$\frac{a x^2 - b x^3 - 603 x^2}{9 a x^7 - 2 x^3}$$ (assuming 603 is a number, not 6 0 3). 9. Factor numerator and denominator if possible. Without exact grouping, simplification might be limited. 10. Problem: Simplify $$3 m x - m x^2 x - 3 m y + 3 m y^2 - m x^2 - 3 m y + 3 m x^2$$. 11. Combine like terms carefully: - Combine $$- m x^2 x$$ as $$- m x^3$$. - Combine $$3 m x^2$$ and $$- m x^2$$ and $$3 m x^2$$. - Combine $$- 3 m y$$ and $$- 3 m y$$. Simplified expression is $$3 m x - m x^3 - 6 m y + 5 m x^2 + 3 m y^2$$. 12. Problem: Simplify the expression $$\frac{x - y}{12} + \frac{2 x + y}{15} + \frac{x - y}{30}$$. 13. Find a common denominator. The denominators 12,15,30 have least common multiple 60. 14. Rewrite each fraction: - $$\frac{x - y}{12} = \frac{5(x - y)}{60}$$ - $$\frac{2 x + y}{15} = \frac{4(2 x + y)}{60}$$ - $$\frac{x - y}{30} = \frac{2(x - y)}{60}$$ 15. Sum numerator terms: $$5(x - y) + 4(2 x + y) + 2(x - y) = 5x - 5y + 8x + 4y + 2x - 2y = (5x + 8x + 2x) + (-5y + 4y - 2y) = 15x - 3y$$. 16. Final simplified expression: $$\frac{15x - 3y}{60} = \frac{3(5x - y)}{60} = \frac{5x - y}{20}$$. 17. Problem: Solve $$\frac{1 - x}{2} - \frac{1 + x}{3} = \frac{2 x}{3}$$. 18. Multiply both sides by 6 to eliminate denominators: $$3(1 - x) - 2(1 + x) = 4 x$$. 19. Simplify: $$3 - 3x - 2 - 2x = 4x$$ $$ (3 - 2) - (3x + 2x) = 4x$$ $$1 - 5x = 4x$$ 20. Add 5x to both sides: $$1 = 9x$$ 21. Divide both sides by 9: $$x = \frac{1}{9}$$. Final answer: $$x = \frac{1}{9}$$. 22. Problem count: 5 unique problems with full answers (problems 1, 6, 7, and parts of 10). Others either incomplete or data statements.