8. Factorise each of the following expressions. (a) \( x(x-5)+6 \) (b) \( x^{2}+3(x-6) \) (c) \( (x-3)^{2}+12 x \) (d) \( (x+3)(x-4)-8 \) (e) \( (3 x-4)(2 x-5)+8(2 x-5) \) (f) \( (3 x-4)^{2}-(2 x+1)^{2} \)

\( \frac{x}{a-b+c}=\frac{y}{b-c+a}=\frac{z}{c-a+b} \) Demons trates That \( \frac{x+y}{a}=\frac{y+z}{b} \)

\( \frac{x}{a-b+c}=\frac{y}{b-c+a}=\frac{z}{c-a+b} \) Demons trates That \( \frac{x+y}{a}=\frac{y+z}{b} \)

2. Solve for \( x \) in the equation : \( ^{\log _{3}(5 x+2)-} \) \( \log _{3}(x-2)=2 \)

Варнант 3 1. Выполните действия \( \begin{array}{ll}\frac{2 x+8}{6 x-12}+\frac{6-2 x}{4 x-8} & \frac{2 x+8}{4 x-12}-\frac{2 x-2}{x-3} \\ \frac{52 x^{9}}{102 y^{7}} \cdot \frac{68 y^{5}}{78 x^{6}} & \frac{64 a^{7}}{45 y^{10}}: \frac{6 a^{5}}{135 y^{6}}\end{array} \)

(2) If \( \frac{2}{L}, \frac{2}{m} \) are the two roots of the equation \( 4 x^{2}+3 x-2=0 \), find the quadratic equation of roots \( L, m \).