1Simplify: \( \frac{a^2+2ab+b^2}{a^2-b^2} \)
2Simplify: \( \frac{5a^3-45a}{4a^2-12a} \)
3Simplify: \( \frac{x^2+x-12}{x^2-x-6} \)
4Simplify: \( \frac{(2x+3)^2}{4x^2-9} \)
5Simplify: \( \frac{3}{x+2}-\frac{2}{x+2} \)
6Simplify: \( \frac{y-15}{y^2-9}+\frac{18}{y^2-9} \)
7Simplify: \( \frac{5p^2}{4-p}-\frac{35p-60}{4-p} \)
8Simplify: \( \frac{1}{2a}-\frac{1}{3a} \)
9Simplify: \( \frac{2}{x-y}+\frac{3}{x+y} \)
10Simplify: \( \frac{x}{2(x-2)}-\frac{1}{x-2} \)
11Simplify: \( \frac{7a^2b}{8c}\times\frac{4c^2}{14ab^2} \)
12Simplify: \( \frac{a^2-b^2}{a}\div\frac{a-b}{b} \)
13Simplify: \( \frac{x^2-5x+6}{x^2-9}\div\frac{x-3}{x+3} \)
14Simplify: \( \frac{2x}{5y}\times\left(\frac{2y}{5}\div\frac{y}{3}\right) \)
15A rectangle has breadth \( x-2 \) units and area \( x^2+3x-10 \) square units. Another rectangle of the same breadth has area \( x^2+x-6 \) square units. Find the length of each rectangle, and the total length when the two are placed together along their breadths.
16Bring \( \frac{x^2-4}{x^2+4x+4} \) to its lowest terms.
17A classmate simplifies \( \frac{x+6}{6} \) and writes the answer as \( x \). Explain why that is wrong.
18Simplify \( \frac{2}{x+1}+\frac{3}{x-1} \).