$\frac{x}{3} + \frac{x}{6} = 1$ |* 6
2x + x = 6
3x = 6
x = 6 : 3
x = 2

$\frac{z}{8} - \frac{z}{4} = 3$ |* 8
z − 2z = 24
−z = 24
z = −24

$\frac{y}{2} - \frac{y}{7} = 5$ |* 14
7y − 2y = 70
5y = 70
y = 70 : 5
y = 14

$\frac{x}{5} - 4 = \frac{x}{3}$
$\frac{x}{5} - \frac{x}{3} = 4$ |* 15
3x − 5x = 60
−2x = 60
x = 60 : (−2)
x = −30

$\frac{y}{3} = \frac{y}{2} - 7$
$\frac{y}{3} - \frac{y}{2} = -7$ |* 6
2y − 3y = −42
−y = −42
y = 42

$\frac{x}{2} - 1 = \frac{x}{3} - 4$
$\frac{x}{2} - \frac{x}{3} = 1 - 4$
$\frac{x}{2} - \frac{x}{3} = -3$ |* 6
3x − 2x = −18
x = −18

$\frac{z}{5} = \frac{z}{10} + 1$
$\frac{z}{5} - \frac{z}{10} = 1$ |* 10
2z − z = 10
z = 10

$\frac{u}{2} - 3 = \frac{u}{4} + 5$
$\frac{u}{2} - \frac{u}{4} = 5 + 3$
$\frac{u}{2} - \frac{u}{4} = 8$ |* 4
2u − u = 32
u = 32