$a)\frac{x+2}{3}=2y\mid \cdot 3$

$x+2=6y\mid \cdot -2$

 

$x=6y-2$

 

$b)\frac{x-3}{a}=-\frac{2}{3}\left(a\ne 0\right)$

$\frac{x-3}{a}=-\frac{2}{3}\mid \cdot a$

$x-3=-\frac{2}{3}a\mid +3$

$x=-\frac{2}{3}a+3$

 

 

$c)\frac{5}{x-1}=\frac{c}{3}\left(x\ne 1\right)$

$\frac{5}{x-1}=\frac{c}{3}\mid \cdot \left(x-1\right)$

$5=\frac{c\left(x-1\right)}{3}\mid \cdot 3$

$15=c\left(x-1\right)\mid :c$

$\frac{15}{c}=x-1\mid +1$

$\frac{15}{c}+1=x$

$x=\frac{15}{c}+1$

 

 

$d)-\frac{4}{dx}=-\frac{2}{d-2}\mid \cdot dx\left(d\ne 0x\ne 0d\ne 2\right)$

$-4=\frac{-2dx}{d-2}\mid :\left(-2d\right)$

$\frac{-4}{-2d}=\frac{x}{d-2}\mid \cdot \left(d-2\right)$

$\frac{2}{d}\cdot \left(d-2\right)=x$

$x=\frac{2\cdot \left(d-2\right)}{d}$

 

 

$e)\frac{3}{p+1}=\frac{a}{x+6}\mid \cdot \left(x+6\right)\left(p\ne -1x\ne -6\right)$

 

   $\frac{3\left(x+6\right)}{p+1}=a\mid \cdot \left(p+1\right)$  

$3\left(x+6\right)=a\left(p+1\right)$  

$3x+18=a\left(p+1\right)\mid -18$  

$3x=a\left(p+1\right)-18\mid :3$  

$x=\frac{a\left(p+1\right)}{3}-6$  

$f)\frac{a-2}{x+6}=\frac{c-1}{b+2}\mid \cdot \left(x+6\right)\left(x\ne -6b\ne -2\right)$

$\left(a-2\right)=\frac{\left(c-1\right)\left(x+6\right)}{b+2}\mid \cdot \left(b+2\right)$

$\left(a-2\right)\left(b+2\right)=\left(c-1\right)\left(x+6\right)\mid :\left(c-1\right)$

$\frac{\left(a-2\right)\left(b+2\right)}{c-1}=x+6$

$\frac{\left(a-2\right)\left(b+2\right)}{c-1}=x+6\mid -6$

$\frac{\left(a-2\right)\left(b+2\right)}{c-1}-6=x$

$x=\frac{\left(a-2\right)\left(b+2\right)}{c-1}-6$