![\frac{x-5}{x+6}- \frac{x+6}{x-5}=0](https://tex.z-dn.net/?f=+%5Cfrac%7Bx-5%7D%7Bx%2B6%7D-++%5Cfrac%7Bx%2B6%7D%7Bx-5%7D%3D0)
![\frac{(x-5)(x-5)-(x+6)(x+6)}{(x+6)(x-5)} = \frac{(x-5)^{2}-(x+6)^2}{(x+6)(x-5)}= \frac{x^2-10x+25-x^2-12x-36}{(x+6)(x-5)}=](https://tex.z-dn.net/?f=++%5Cfrac%7B%28x-5%29%28x-5%29-%28x%2B6%29%28x%2B6%29%7D%7B%28x%2B6%29%28x-5%29%7D+%3D++%5Cfrac%7B%28x-5%29%5E%7B2%7D-%28x%2B6%29%5E2%7D%7B%28x%2B6%29%28x-5%29%7D%3D+%5Cfrac%7Bx%5E2-10x%2B25-x%5E2-12x-36%7D%7B%28x%2B6%29%28x-5%29%7D%3D)
![= \frac{-22x-11}{x^2-5x+6x-30}= \frac{-22x-11}{x^2+x-30}=0](https://tex.z-dn.net/?f=%3D+%5Cfrac%7B-22x-11%7D%7Bx%5E2-5x%2B6x-30%7D%3D+%5Cfrac%7B-22x-11%7D%7Bx%5E2%2Bx-30%7D%3D0)
Дробь будет равна нулю если числитель будет равен нулю (знаменатель не может быть равен нулю, на ноль делить нельзя)
-22x-11=0
-22x=11
x=-11/22=-1/2
![\frac{2}{x-1}+3= \frac{1}{x+1}](https://tex.z-dn.net/?f=+%5Cfrac%7B2%7D%7Bx-1%7D%2B3%3D+%5Cfrac%7B1%7D%7Bx%2B1%7D)
![\frac{2}{x-1}+3- \frac{1}{x+1}=0](https://tex.z-dn.net/?f=+%5Cfrac%7B2%7D%7Bx-1%7D%2B3-+%5Cfrac%7B1%7D%7Bx%2B1%7D%3D0)
Приводим к общему знаменателю, который представляет из себя разность квадратов (x²-1)
![\frac{2(x+1)+3(x^2-1)-(x-1)}{x^2-1}=0](https://tex.z-dn.net/?f=+%5Cfrac%7B2%28x%2B1%29%2B3%28x%5E2-1%29-%28x-1%29%7D%7Bx%5E2-1%7D%3D0)
![\frac{2x+2+3x^2-3-x+1}{x^2-1}=0](https://tex.z-dn.net/?f=+%5Cfrac%7B2x%2B2%2B3x%5E2-3-x%2B1%7D%7Bx%5E2-1%7D%3D0)
![\frac{3x^2+x}{x^2-1}=0](https://tex.z-dn.net/?f=+%5Cfrac%7B3x%5E2%2Bx%7D%7Bx%5E2-1%7D%3D0)
3x²+x=0
x(3x+1)=0
x=0 3x+1=0
3x=-1
x=-1/3
Получилось два корня 0 и =-1/3
![\frac{1-2x}{x^2-1}- \frac{1}{x+1} = \frac{2}{x-1}](https://tex.z-dn.net/?f=+%5Cfrac%7B1-2x%7D%7Bx%5E2-1%7D-+%5Cfrac%7B1%7D%7Bx%2B1%7D+%3D+%5Cfrac%7B2%7D%7Bx-1%7D+)
![\frac{1-2x}{x^2-1}- \frac{1}{x+1}- \frac{2}{x-1}=0](https://tex.z-dn.net/?f=+%5Cfrac%7B1-2x%7D%7Bx%5E2-1%7D-+%5Cfrac%7B1%7D%7Bx%2B1%7D-+%5Cfrac%7B2%7D%7Bx-1%7D%3D0+)
Приводим к общему знаменателю, им будет (x²-1) - разность квадратов
![\frac{1-2x-(x-1)-2(x+1)}{x^2-1}=0](https://tex.z-dn.net/?f=+%5Cfrac%7B1-2x-%28x-1%29-2%28x%2B1%29%7D%7Bx%5E2-1%7D%3D0)
![\frac{1-2x-x+1-2x-1}{x^2-1}=0](https://tex.z-dn.net/?f=+%5Cfrac%7B1-2x-x%2B1-2x-1%7D%7Bx%5E2-1%7D%3D0)
![\frac{1-5x}{x^2-1}=0](https://tex.z-dn.net/?f=+%5Cfrac%7B1-5x%7D%7Bx%5E2-1%7D%3D0)
1-5x=0
-5x=-1
x=1/5
![4 \frac{1}{4}- \frac{x+1}{x-2}= \frac{x-2}{x+1}](https://tex.z-dn.net/?f=4+%5Cfrac%7B1%7D%7B4%7D-+%5Cfrac%7Bx%2B1%7D%7Bx-2%7D%3D+%5Cfrac%7Bx-2%7D%7Bx%2B1%7D+)
<span>
![\frac{17}{4}- \frac{x+1}{x-2}- \frac{x-2}{x+1}=0](https://tex.z-dn.net/?f=+%5Cfrac%7B17%7D%7B4%7D-+%5Cfrac%7Bx%2B1%7D%7Bx-2%7D-+%5Cfrac%7Bx-2%7D%7Bx%2B1%7D%3D0)
Приводим к общему знаменателю, который будет 4(x-2</span>)(x+1)
![\frac{17(x-2)(x+1)-4(x+1)(x+1)-4(x-2)(x-2)}{4(x-2)(x+1)}=0](https://tex.z-dn.net/?f=+%5Cfrac%7B17%28x-2%29%28x%2B1%29-4%28x%2B1%29%28x%2B1%29-4%28x-2%29%28x-2%29%7D%7B4%28x-2%29%28x%2B1%29%7D%3D0)
![\frac{17x^2+17x-34x-34-4x^2-4x-4x-4-4x^2+8x+8x-16}{4(x-2)(x+1)}=0](https://tex.z-dn.net/?f=+%5Cfrac%7B17x%5E2%2B17x-34x-34-4x%5E2-4x-4x-4-4x%5E2%2B8x%2B8x-16%7D%7B4%28x-2%29%28x%2B1%29%7D%3D0)
![\frac{9x^2-9x-54}{4(x-2)(x+1)}=0](https://tex.z-dn.net/?f=+%5Cfrac%7B9x%5E2-9x-54%7D%7B4%28x-2%29%28x%2B1%29%7D%3D0)
9x²-9x-54=0
D=(-9)²-4*9*(-54)=81+1944=2025
![x_{1}= \frac{9- \sqrt{2025}}{2*9}= \frac{9-45}{18}=-2](https://tex.z-dn.net/?f=+x_%7B1%7D%3D+%5Cfrac%7B9-+%5Csqrt%7B2025%7D%7D%7B2%2A9%7D%3D+%5Cfrac%7B9-45%7D%7B18%7D%3D-2)
![x_{2}= \frac{9+45}{18}=3](https://tex.z-dn.net/?f=+x_%7B2%7D%3D+%5Cfrac%7B9%2B45%7D%7B18%7D%3D3)
(12целых 2/9дробью+24целых 2/3дробью-16целых 2/15дробью):2=
1)(4x-0,2y)²=16x²-2*4x*0,2y+0,04y²=<span><span>16x²-1,6xy+0,04y²
</span>2)(2/7y+x)(x-2/7y)</span>=(x-2/7y)(x-2/7y)=x²-<span>(2/7y)²=x²-4/49y²
</span><span>2(x-2)(x+2)-(x-1)²=x²-5
</span><span>2(x²-4)-(x²-2x+1)=x²-5
</span><span>2x²-8-x²+2x-1=x²-5
</span><span>x²-9+2x=x²-5
</span><span>x²+2x-x²=-5+9
</span><span>2x=4
x=2
</span>(a²+10a+25)/(a+5)=<span>(a+5)²/(a+5)=</span><span>a+5=</span>-2,5+5=<span>2,5</span>