!!!!!!!!!!!!!!!!!!!!!!!!!!!!
(x-4)/(x+6)²)-(x+1)/(x-6)(x+6)=
=((x-4)(x-6)-(x+1)(x+6))/(x-6)(x+6)²=(х²-10x+24-х²-7x-6)/(x-6)(x+6)²=(-17x+18)/(x-6)(x+6)²=(-7.5)/(-4.5)(7.5)²=
=-1/(-4.5)=1/4.5
![y = \frac{1}{4}x^4 - \frac{2}{3}x^3](https://tex.z-dn.net/?f=y+%3D++%5Cfrac%7B1%7D%7B4%7Dx%5E4+-++%5Cfrac%7B2%7D%7B3%7Dx%5E3)
![y' = \frac{1}{4}*4x^3 - \frac{2}{3}*3x^2](https://tex.z-dn.net/?f=y%27+%3D++%5Cfrac%7B1%7D%7B4%7D%2A4x%5E3+-++%5Cfrac%7B2%7D%7B3%7D%2A3x%5E2)
![y' = x^3 - 2x^2](https://tex.z-dn.net/?f=y%27+%3D+x%5E3+-+2x%5E2)
![x^3 - 2x^2 = 0](https://tex.z-dn.net/?f=x%5E3+-+2x%5E2+%3D+0)
![X^2(x -2) = 0 \\ x^2 = 0 \\ x = 0](https://tex.z-dn.net/?f=X%5E2%28x+-2%29+%3D+0+%5C%5C+x%5E2+%3D+0+%5C%5C+x+%3D+0)
![x = 2](https://tex.z-dn.net/?f=x+%3D+2)
Прямая со знаками и прочим во вложениях
x max = 0 => ymax= y(0) = 0
xmin = 2 => ymin = y(2) =
![-\frac{4}{3}](https://tex.z-dn.net/?f=-%5Cfrac%7B4%7D%7B3%7D+)
y возрастает (-Б; 0) U (2;+Б)
y убывает (0;2)
Знаменатель дроби не должен равняться нулю, так как на ноль делить нельзя.
![1)\frac{x-1}{x^{2}-4 } \\\\x^{2}-4\neq 0\\\\x^{2}\neq4\\\\x_{1} \neq2;x_{2}\neq -2\\\\Otvet:\boxed {x\in(-\infty;-2)\cup(-2;2)\cup(2;+\infty)}](https://tex.z-dn.net/?f=1%29%5Cfrac%7Bx-1%7D%7Bx%5E%7B2%7D-4%20%7D%20%5C%5C%5C%5Cx%5E%7B2%7D-4%5Cneq%200%5C%5C%5C%5Cx%5E%7B2%7D%5Cneq4%5C%5C%5C%5Cx_%7B1%7D%20%5Cneq2%3Bx_%7B2%7D%5Cneq%20-2%5C%5C%5C%5COtvet%3A%5Cboxed%20%7Bx%5Cin%28-%5Cinfty%3B-2%29%5Ccup%28-2%3B2%29%5Ccup%282%3B%2B%5Cinfty%29%7D)
![2)\frac{x+2}{x^{2}-25}\\\\x^{2}-25\neq 0\\\\x^{2} \neq 25\\\\x_{1}\neq-5;x_{2} \neq 5\\\\Otvet:\boxed {x\in(-\infty;-5)\cup(-5;5)\cup(5;+\infty)}](https://tex.z-dn.net/?f=2%29%5Cfrac%7Bx%2B2%7D%7Bx%5E%7B2%7D-25%7D%5C%5C%5C%5Cx%5E%7B2%7D-25%5Cneq%200%5C%5C%5C%5Cx%5E%7B2%7D%20%5Cneq%2025%5C%5C%5C%5Cx_%7B1%7D%5Cneq-5%3Bx_%7B2%7D%20%5Cneq%205%5C%5C%5C%5COtvet%3A%5Cboxed%20%7Bx%5Cin%28-%5Cinfty%3B-5%29%5Ccup%28-5%3B5%29%5Ccup%285%3B%2B%5Cinfty%29%7D)
A1=3+5=8
a2=3*2+5=11
d=3
s8=4 (2a1+7d)= 4 ( 16+21)=4*37=148
s8=148