$(\frac{x}{2} - \frac{x}{3})^2 - 25 = 0$
$(\frac{x}{2} - \frac{x}{3} - 5)(\frac{x}{2} - \frac{x}{3} + 5) = 0$
$(\frac{3x}{6} - \frac{2x}{6} - 5)(\frac{3x}{6} - \frac{2x}{6} + 5) = 0$
$(\frac{x}{6} - 5)(\frac{x}{6} + 5) = 0$
$\frac{x}{6} - 5 = 0$
$\frac{x}{6} = 5$
x = 5 * 6
x = 30
или
$\frac{x}{6} + 5 = 0$
$\frac{x}{6} = -5$
x = −5 * 6
x = −30
Ответ: −30; 30.

$(\frac{x}{2} - \frac{x}{4})^2 - 9 = 0$
$(\frac{x}{2} - \frac{x}{4} - 3)(\frac{x}{2} - \frac{x}{4} + 3) = 0$
$(\frac{2x}{4} - \frac{x}{4} - 3)(\frac{2x}{4} - \frac{x}{4} + 3) = 0$
$(\frac{x}{4} - 3)(\frac{x}{4} + 3) = 0$
$\frac{x}{4} - 3 = 0$
$\frac{x}{4} = 3$
x = 3 * 4
x = 12
или
$\frac{x}{4} + 3 = 0$
$\frac{x}{4} = -3$
x = −3 * 4
x = −12
Ответ: −12; 12.

$4 - (x - \frac{x}{5})^2 = 0$
$(2 - x + \frac{x}{5})(2 + x - \frac{x}{5}) = 0$
(10 − 5x + x)(10 + 5x − x) = 0
(10 − 4x)(10 + 4x) = 0
10 − 4x = 0
−4x = −10
x = 2,5
или
10 + 4x = 0
4x = −10
x = −2,5
Ответ: −2,5; 2,5.

$1 - (\frac{x}{3} - \frac{x}{5})^2 = 0$
$(1 - \frac{x}{3} + \frac{x}{5})(1 + \frac{x}{3} - \frac{x}{5}) = 0$
(15 − 5x + 3x)(15 + 5x − 3x) = 0
(15 − 2x)(15 + 2x) = 0
15 − 2x = 0
−2x = −15
x = 7,5
или
15 + 2x = 0
2x = −15
x = −7,5
Ответ: −7,5; 7,5.