(Solved): 1. Simplify the following algebraic fractions. a) \( \frac{2}{x-6}+\frac{6}{x-3}= \) b) \( \frac{x ...

1. Simplify the following algebraic fractions. a) \( \frac{2}{x-6}+\frac{6}{x-3}= \) b) \( \frac{x}{5 x-3}-\frac{4 x}{5 x+1}= \) c) \( \frac{x+1}{3}-\frac{x-1}{4}= \) d) \( \frac{2 a}{15}-\frac{a}{3}+\frac{2 a}{5}= \) :ase-1: LHS and/or RHS will have more than one Single Fraction 2. Simplify and solve the following algebraic equations by the appropriate method (Linear Equation/Quadratic Equation). a) \( \frac{6 x-3}{2}+\frac{2 x+9}{6}=20 \) b) \( \frac{1}{x+3}-\frac{6}{x+5}=-1 \) c) \( \frac{x}{x-2}-\frac{4}{x+3}=1 \) d) \( \frac{1}{3 x+5}+\frac{1}{4 x-3}=4 \) e) \( \frac{2}{x-2}+\frac{4}{x+1}=3 \) f) \( \frac{x+3}{x+2}+\frac{x-6}{5 x-8}=1 \) Case-2: LHS and RHS will have a single fraction and/or a number 3. Simplify and solve the following algebraic equations by the appropriate method (Linear Equation/Quadratic Equation). a) \( \frac{7 x-1}{4}=5 \) b) \( \frac{5}{x+3}=\frac{6}{x+5} \) c) \( \frac{3 x-2}{2 x-1}=\frac{x+6}{x+4} \) d) \( \frac{4 x+3}{5 x-9}=\frac{x-2}{x-9} \) e) \( \frac{3 x-2}{2 x-3}=\frac{x-6}{x-3} \) f) \( \frac{2 x+1}{x}=-1 \) g) \( x=\frac{12}{2 x+5} \) h) \( \frac{x-4}{x+8}=\frac{x}{2} \) i) \( \frac{2 x}{5}=4 \)