Задача 74572 x+10 / x-0,5 = x+10 / 0,5x-5...

650d9c70f87368773aa885f2

12/5/2023 10:59:38 AM

x+10 / x-0,5 = x+10 / 0,5x-5

626fab9a354ab65fb2f43abb

12/5/2023 11:04:25 AM

★

(x + 10)/(x - 0,5) = (x + 10)/(0,5x - 5)
По правилу пропорции:
(x + 10)(0,5x - 5) = (x - 0,5)(x + 10)
(x + 10)(0,5x - 5) - (x - 0,5)(x + 10) = 0
(x + 10)(0,5x - 5 - x + 0,5) = 0
(x + 10)(-0,5x - 4,5) = 0
x1 = -10
x2 = 4,5/(-0,5) = -9

5f3ea7e3faf909182968ddd9

12/5/2023 11:07:55 AM

[m]\frac{x+10}{x-0,5}=\frac{x+10}{0,5x-5}[/m]

[m]\frac{x+10}{x-0,5}-\frac{x+10}{0,5x-5}=0[/m]

[m]\frac{(x+10)(0,5x-5)-(x+10)(x-0,5)}{(x-0,5)(0,5x-5)}=0[/m]

[m]\frac{(x+10)((0,5x-5)-(x-0,5))}{(x-0,5)(0,5x-5)}=0[/m]

[m]\frac{(x+10)(0,5x-5-x+0,5)}{(x-0,5)(0,5x-5)}=0[/m]

[m]\frac{(x+10)(-0,5x-4,5)}{(x-0,5)(0,5x-5)}=0[/m]

[m]\left\{\begin {matrix}(x+10)(-0,5x-4,5)=0\\(x-0,5)(0,5x-5) ≠ 0\end {matrix}\right.[/m]

[m]\left\{\begin {matrix}x+10=0\\x-0,5≠ 0; (0,5x-5) ≠ 0\end {matrix}\right.[/m] или [m]\left\{\begin {matrix}-0,5x-4,5=0\\x-0,5≠ 0; (0,5x-5) ≠ 0\end {matrix}\right.[/m]

[m]\left\{\begin {matrix}x=-10\\x≠ 0,5; x ≠ 10\end {matrix}\right.[/m] или [m]\left\{\begin {matrix}x=4,5:(-0,5)\\x≠ 0,5; x ≠ 10\end {matrix}\right.[/m]

[m]\left\{\begin {matrix}x=-10\\x≠ 0,5; x ≠ 10\end {matrix}\right.[/m] или [m]\left\{\begin {matrix}x=-9\\x≠ 0,5; x ≠ 10\end {matrix}\right.[/m]

О т в е т. [b]-9; 10[/b]