Вроде видно
Скорее всего так
(2x-2)(2x+2)+2x²=2
4x²-4+2x²=2
6x²=6
x²=1
x=1 и х=-1 1>-1
Ответ: 1
Задание: <span>Найдите значение выражения
</span>
![\frac{ \frac{y}{5x} - \frac{5x}{y} } {y+5x}](https://tex.z-dn.net/?f=+%5Cfrac%7B+%5Cfrac%7By%7D%7B5x%7D+-+%5Cfrac%7B5x%7D%7By%7D+%7D+%7By%2B5x%7D+)
<span>
х=
![\frac{1}{7}](https://tex.z-dn.net/?f=+%5Cfrac%7B1%7D%7B7%7D+)
у=</span>
![\frac{1}{4}](https://tex.z-dn.net/?f=+%5Cfrac%7B1%7D%7B4%7D+)
1. Приведем дроби в числителе к общему знаменателю 5xy:
![\frac{y}{5x}](https://tex.z-dn.net/?f=+%5Cfrac%7By%7D%7B5x%7D+)
-
![\frac{5x}{y}](https://tex.z-dn.net/?f=+%5Cfrac%7B5x%7D%7By%7D+)
=
![\frac{5x y^{2} }{5xy}](https://tex.z-dn.net/?f=+%5Cfrac%7B5x+y%5E%7B2%7D+%7D%7B5xy%7D+)
-
![\frac{25 x^{2} y}{5xy}](https://tex.z-dn.net/?f=+%5Cfrac%7B25+x%5E%7B2%7D+y%7D%7B5xy%7D+)
=
![\frac{ y^{2} }{5xy}](https://tex.z-dn.net/?f=+%5Cfrac%7B+y%5E%7B2%7D+%7D%7B5xy%7D)
-
![\frac{25 x^{2} }{5xy}](https://tex.z-dn.net/?f=+%5Cfrac%7B25+x%5E%7B2%7D+%7D%7B5xy%7D+)
=
![\frac{ y^{2}-25 x^{2} }{5xy}](https://tex.z-dn.net/?f=+%5Cfrac%7B+y%5E%7B2%7D-25+x%5E%7B2%7D+%7D%7B5xy%7D+)
2. Разложим числитель: y²-25x²=(y-5x)(y+5x)
3. Подставим:
![\frac{(y-5x)(y+5x)}{5xy}](https://tex.z-dn.net/?f=+%5Cfrac%7B%28y-5x%29%28y%2B5x%29%7D%7B5xy%7D+)
=
![\frac{(y-5x)(y+5x)}{5xy}](https://tex.z-dn.net/?f=+%5Cfrac%7B%28y-5x%29%28y%2B5x%29%7D%7B5xy%7D+)
4.
![\frac{(y-5x)(y+5x)}{5xy}](https://tex.z-dn.net/?f=+%5Cfrac%7B%28y-5x%29%28y%2B5x%29%7D%7B5xy%7D+)
: (y+5x) =
![\frac{(y-5x)(y+5x)}{5xy(y+5x)}](https://tex.z-dn.net/?f=+%5Cfrac%7B%28y-5x%29%28y%2B5x%29%7D%7B5xy%28y%2B5x%29%7D+)
=
![\frac{y-5x}{5xy}](https://tex.z-dn.net/?f=+%5Cfrac%7By-5x%7D%7B5xy%7D+)
5. Подставим числовые значения:
<span>х=
![\frac{1}{7}](https://tex.z-dn.net/?f=+%5Cfrac%7B1%7D%7B7%7D+)
у=</span>
Числитель:
y-5x=
![\frac{1}{4}](https://tex.z-dn.net/?f=+%5Cfrac%7B1%7D%7B4%7D+)
- 5*
![\frac{1}{7}](https://tex.z-dn.net/?f=+%5Cfrac%7B1%7D%7B7%7D+)
=
![\frac{1}{4}](https://tex.z-dn.net/?f=+%5Cfrac%7B1%7D%7B4%7D+)
-
![\frac{5}{7}](https://tex.z-dn.net/?f=+%5Cfrac%7B5%7D%7B7%7D+)
=
![\frac{7}{28}](https://tex.z-dn.net/?f=+%5Cfrac%7B7%7D%7B28%7D+)
-
![\frac{20}{28}](https://tex.z-dn.net/?f=+%5Cfrac%7B20%7D%7B28%7D+)
= -
![\frac{13}{28}](https://tex.z-dn.net/?f=+%5Cfrac%7B13%7D%7B28%7D+)
Знаменатель:
5ху=5×
![\frac{1}{4}](https://tex.z-dn.net/?f=+%5Cfrac%7B1%7D%7B4%7D+)
×
![\frac{1}{7}](https://tex.z-dn.net/?f=+%5Cfrac%7B1%7D%7B7%7D+)
=
(-
![\frac{13}{28}](https://tex.z-dn.net/?f=+%5Cfrac%7B13%7D%7B28%7D+)
):
![\frac{5}{28}](https://tex.z-dn.net/?f=+%5Cfrac%7B5%7D%7B28%7D+)
=
![\frac{(-13)*28}{28*5}](https://tex.z-dn.net/?f=+%5Cfrac%7B%28-13%29%2A28%7D%7B28%2A5%7D+)
=
![\frac{-13*1}{1*5}](https://tex.z-dn.net/?f=+%5Cfrac%7B-13%2A1%7D%7B1%2A5%7D+)
=
![\frac{-13}{5}](https://tex.z-dn.net/?f=+%5Cfrac%7B-13%7D%7B5%7D+)
= - 2
![\frac{3}{5}](https://tex.z-dn.net/?f=+%5Cfrac%7B3%7D%7B5%7D+)
= -2,6
У=12-5(2x-1)-3(5-4x)
y=12-10x+5-15+12x
y=2+2x