(1) \( \frac{a b+b c}{b}= \) (2) \( \frac{a^{2}+a b}{a}= \) (3) \( \frac{a^{2}+2 a}{a}= \) (4) \( \frac{a^{2}+a}{a}=\frac{\square}{a}+\frac{\square}{a}=\square+1 \) (5) \( \frac{5 x^{2}+x}{x}= \) (6) \( \frac{a b^{2}-a b c+a b}{a b}= \) (7) \( \frac{6 x^{3}-2 x^{2}+2 x}{2 x}= \) (7) (5) (5)

Let's break these down in a way that's both informative and enjoyable! When working through these algebraic expressions, it’s crucial to recognize patterns and simplify effectively. Notice how each expression can often be simplified by factoring out common terms, leading to less clutter in your final answer. It’s like cleaning your room: the more you organize your factors, the easier it is to see what you have on hand! In real-world applications, simplifying expressions is a valuable skill, especially in fields like engineering, economics, and computer science. Whether you're calculating material costs or tweaking algorithms, the ability to break down complex formulas into manageable parts can save time and make problem-solving much more efficient. After all, no one wants to get lost in a sea of equations!