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$1. \\ a) \frac{6-x}{x+3}= \frac{7x+9}{3+x} \\ 6-x=7x+9 \\ -8x=3 \\ x= -\frac{3}{8} \\ \\ b) \frac{8x-3}{5-x} = \frac{2x-1}{x-5} \\ \frac{8x-3}{x-5}=- \frac{2x-1}{x-5} \\ 8x-3=-2x+1 \\ 10x=4 \\ x= \frac{4}{10}= \frac{2}{5} \\ \\ 2. \\ a) \frac{19-22x}{13-2x}=-5 \\ 19-22x=-5(13-2x) \\ 19-22x=-65+10x \\ -32x=-84 \\ x= \frac{84}{32}= \frac{21}{8}$

$b) \frac{24x^2+37}{2-x}=17 \\ 24x^2+37=17(2-x) \\ 24x^2+17x+3=0 \\ D=289-288=1 \\ x_{1} = \frac{-17-1}{48}= -\frac{3}{8} \\ x_{2}= \frac{-17+1}{48}=- \frac{1}{3} \\ \\ 3. \\ a) \frac{x}{1,6-x}= \frac{5}{5x+1} \\ 5x(5x+1)=5(8-5x) \\ 5(5x^2+6x-8)=0 \\ 5x^2+6x-8=0 \\ D=36+160=196=14^2 \\ x_{1}= \frac{-6-14}{10}=-2 \\ x_{2}= \frac{-6+14}{10}= \frac{8}{10}= \frac{4}{5}$

$b) \frac{3x+4}{1-3x^2}= \frac{4}{x} \\ (3x+4)x=4(1-3x^2) \\ 15x^2+4x-4=0 \\ D=16+240=256=16^2 \\ x_{1} = \frac{-4-16}{30}=- \frac{2}{3} \\ x_{2}= \frac{-4+16}{30}= \frac{2}{5} \\ \\ 4. \\ \frac{3-3x}{x}=11-11x \\ 3-3x=x(11-11x)} \\ 11x^2-14x+3=0 \\ D=196-132=64=8^2 \\ x_{1}= \frac{14-8}{22} = \frac{3}{11} \\ x_{2}= \frac{14+8}{22}=1$