a) $\frac{5}{x-10}=-\frac{3}{1-2x}/\cdot \left(x-10\right)\left(1-2x\right)$

$5\left(1-2x\right)=-3\left(x-10\right)$

$5-10x=-3x+30$

$-7x=25$

$x=-3\frac{4}{7}$

b) $\frac{2}{6}=\frac{2x+1}{7x-2}/\cdot 6\left(7x-2\right)$

$2\left(7x-2\right)=6\left(2x+1\right)$

$14x-4=12x+6$

$2x=10$

$x=5$

c) $\frac{6}{9x+2}=\frac{4}{6x+1}/\cdot \left(9x+2\right)\left(6x+1\right)$

$6\left(6x+1\right)=4\left(9x+2\right)$