Только при a=0 функция ax^2+5x+1 вырождается и становится линейной 5x+1
√500 х + √20 х - √80 х = 10√5 x +2√5 x - 4√5 x = 8√5 x
![(\frac {6}{y^2-9}+\frac {1}{3-y}) \cdot (\frac {y^2+6y+9}{5}) \\ \\ \\ \\ 1) \ \frac {6}{y^2-9}+\frac {1}{3-y}=\frac {6}{(y-3)(y+3)}+\frac {1}{3-y}=\frac {6}{(y-3)(y+3)}-\frac {1}{y-3}= \\ \\ =\frac {6}{(y-3)(y+3)}-\frac {3+y}{(y-3)(y+3)}=\frac {6-(3+y)}{(y-3)(y+3)}=\frac {6-3-y}{(y-3)(y+3)}=\\ \\ =\frac {3-y}{(y-3)(y+3)}= -\frac {1}{3+y} \\ \\ \\ 2) -\frac {1}{3+y} \cdot \frac {y^2+6y+9}{5}=- \frac {1}{3+y} \cdot \frac {(y+3)^2}{5}=-\frac {1 \cdot (y+3)(y+3)}{(3+y) \cdot 5}=-\frac {y+3}{5}](https://tex.z-dn.net/?f=%28%5Cfrac+%7B6%7D%7By%5E2-9%7D%2B%5Cfrac+%7B1%7D%7B3-y%7D%29+%5Ccdot+%28%5Cfrac+%7By%5E2%2B6y%2B9%7D%7B5%7D%29+%5C%5C+%5C%5C+%5C%5C+%5C%5C+1%29+%5C+%5Cfrac+%7B6%7D%7By%5E2-9%7D%2B%5Cfrac+%7B1%7D%7B3-y%7D%3D%5Cfrac+%7B6%7D%7B%28y-3%29%28y%2B3%29%7D%2B%5Cfrac+%7B1%7D%7B3-y%7D%3D%5Cfrac+%7B6%7D%7B%28y-3%29%28y%2B3%29%7D-%5Cfrac+%7B1%7D%7By-3%7D%3D+%5C%5C+%5C%5C+%3D%5Cfrac+%7B6%7D%7B%28y-3%29%28y%2B3%29%7D-%5Cfrac+%7B3%2By%7D%7B%28y-3%29%28y%2B3%29%7D%3D%5Cfrac+%7B6-%283%2By%29%7D%7B%28y-3%29%28y%2B3%29%7D%3D%5Cfrac+%7B6-3-y%7D%7B%28y-3%29%28y%2B3%29%7D%3D%5C%5C+%5C%5C+%3D%5Cfrac+%7B3-y%7D%7B%28y-3%29%28y%2B3%29%7D%3D+-%5Cfrac+%7B1%7D%7B3%2By%7D+%5C%5C+%5C%5C+%5C%5C+2%29+-%5Cfrac+%7B1%7D%7B3%2By%7D+%5Ccdot+%5Cfrac+%7By%5E2%2B6y%2B9%7D%7B5%7D%3D-+%5Cfrac+%7B1%7D%7B3%2By%7D+%5Ccdot+%5Cfrac+%7B%28y%2B3%29%5E2%7D%7B5%7D%3D-%5Cfrac+%7B1+%5Ccdot+%28y%2B3%29%28y%2B3%29%7D%7B%283%2By%29+%5Ccdot+5%7D%3D-%5Cfrac+%7By%2B3%7D%7B5%7D+)
если в решении что-то неясно, пишите в лс
I. a) ((8/10)^-2 +(6/10)^-2)^-1 =((10²/8²) +(10²/6²))^-1 =(100/64 +100/36)^-1 =(3600+6400)/2304)^-1 =2304/10000 =0.2304
b) =(5/2² -20/5²) :(3²/4²) =(5/4 -4/5) *16/9 =(25 -16)*16 /20*9 =9*16 /20*9 =16/20 =4/5 =0.8
II. =a^-3(1 -a²) /(-a^-2(1 -a²) = -a²/a^3 = -1/a
III. (x^-1 -y^-1)^-2 =(1/x -1/y)^-2 =((y-x)/xy))^-2 =x²y² /(y-x)²
(x^-2 -y^-2)^-1 =(1/x² -1/y²)^-1 =((y²-x²)/x²y²)^-1 =x²y² /(y²-x²) =x²y²/(y-x)(y+x)
x²y² /(y-x)² * (y-x)(y+x)/x²y² =(x²y² *(y-x)(y+x)) /(y-x)² *x²y² =(y+x)/(y-x)
ответ: (y +x) /(y -x)