\begin{tabular}{l|l}\( \frac{x+2}{x+1} \) & 2. Solve tho following equations \\ a. \( \frac{x}{4}-\frac{x}{3}=2 \) \\ b. \( x+\frac{x+5}{3}=7 \) \\ c. \( \frac{m+2}{4}-\frac{m-6}{3}=\frac{1}{2} \) \\ 3. Solve each of the following \\ a. \( (3 x-1)(x+2)=0 \) \\ b \( \left(3 x^{2}-1\right)(x+2)=10 \) \\ c. \( 2 x^{2}-4 x \) \\ d. \( 5 x^{2}+2 x^{2}=3 \) \\ e. \( 3 x^{2}=48 \) \\ f \( x^{2}=9 \) \\ \( 9 . ~ \) & \( 9 x^{2}=x \) \\ h. \( 2 x^{2}-x=10 \) \\ i. \( 3 x^{2}-5 x-2=0 \)\end{tabular}

To really appreciate the beauty of algebra, it's important to note that many brilliant mathematicians throughout history contributed to the development of algebraic thinking. From the ancient Babylonians using geometric methods to solve quadratic equations, to Al-Khwarizmi, who is often called the "father of algebra," the journey has been fascinating! Understanding these roots not only enriches your knowledge but also makes solving equations feel like a continuation of a grand intellectual tradition. When tackling equations, remember that common pitfalls can trip you up. For instance, when you have fractions, don't forget to find a common denominator before subtracting—this will save you from messy mistakes. Similarly, when squaring both sides of an equation, watch out for extraneous solutions that may not satisfy the original equation. A little attention to detail can make all the difference in your problem-solving journey!