17.6×17.6=309.76
2.4×2.4=5.76
309.76-5.76=304
10³=1000
304÷1000=38/125
Вот решение:
3a/4c -(9a²+16c²)/12ac+(4c-9a)/3a = (9a²-9a²-16c²+16c²-36ac)/12ac =
= -36ac/12ac = -3
Ответ: -3
Пусть дробь
![\frac{x}{y}](https://tex.z-dn.net/?f=+%5Cfrac%7Bx%7D%7By%7D+)
Если от числителя и знаменателя дроби отнять число два, то дробь уменьшится на одну восьмую :
![\frac{x-2}{y-2}+ \frac{1}{8}= \frac{x}{y}](https://tex.z-dn.net/?f=+%5Cfrac%7Bx-2%7D%7By-2%7D%2B+%5Cfrac%7B1%7D%7B8%7D%3D+%5Cfrac%7Bx%7D%7By%7D+++)
Если к числителю и знаменателю прибавить по единице, то дробь увеличится на
<span> одну двадцать четвертую:
![</span><span>\frac{x+1}{y+1}- \frac{1}{24}= \frac{x}{y}](https://tex.z-dn.net/?f=%3C%2Fspan%3E%3Cspan%3E%5Cfrac%7Bx%2B1%7D%7By%2B1%7D-+%5Cfrac%7B1%7D%7B24%7D%3D+%5Cfrac%7Bx%7D%7By%7D)
</span>Решаем систему двух уравнений:
![\left \{ {{\frac{x-2}{y-2}+ \frac{1}{8}= \frac{x}{y}} \atop {\frac{x+1}{y+1}- \frac{1}{24}= \frac{x}{y} }} \right. \Rightarrow \left \{ {{\frac{8y(x-2)+y(y-2)-8x(y-2)}{8y(y-2)}=0} \atop {\frac{24y(x+1)-y(y+1)-24x(y+1)}{24y(y+1)}=0}} \right.](https://tex.z-dn.net/?f=+%5Cleft+%5C%7B+%7B%7B%5Cfrac%7Bx-2%7D%7By-2%7D%2B+%5Cfrac%7B1%7D%7B8%7D%3D+%5Cfrac%7Bx%7D%7By%7D%7D+%5Catop%0A+%7B%5Cfrac%7Bx%2B1%7D%7By%2B1%7D-+%5Cfrac%7B1%7D%7B24%7D%3D+%5Cfrac%7Bx%7D%7By%7D+%7D%7D+%5Cright.+%5CRightarrow+%0A%5Cleft+%5C%7B+%7B%7B%5Cfrac%7B8y%28x-2%29%2By%28y-2%29-8x%28y-2%29%7D%7B8y%28y-2%29%7D%3D0%7D+%5Catop+%0A%7B%5Cfrac%7B24y%28x%2B1%29-y%28y%2B1%29-24x%28y%2B1%29%7D%7B24y%28y%2B1%29%7D%3D0%7D%7D+%5Cright.)
Так как у≠0,у-2≠0,у+1≠0, то
![ \left \{ {{8y(x-2)+y(y-2)-8x(y-2)=0} \atop {24y(x+1)-y(y+1)-24x(y+1)=0}} \right.](https://tex.z-dn.net/?f=+%0A%5Cleft+%5C%7B+%7B%7B8y%28x-2%29%2By%28y-2%29-8x%28y-2%29%3D0%7D+%5Catop+%0A%7B24y%28x%2B1%29-y%28y%2B1%29-24x%28y%2B1%29%3D0%7D%7D+%5Cright.)
![\left \{ {{-18y+y ^{2} +16x=0} \atop {+23y-y ^{2} -24x=0}} \Rightarrow \left \{ {{-18y+y ^{2} +16x=0} \atop {5y-8x=0}} \left \{ {{-18\cdot 1,6x+(1,6x) ^{2} +16x=0} \atop {y=1,6x}}](https://tex.z-dn.net/?f=+%5Cleft+%5C%7B+%7B%7B-18y%2By+%5E%7B2%7D+%2B16x%3D0%7D+%5Catop+%7B%2B23y-y+%5E%7B2%7D+-24x%3D0%7D%7D+%5CRightarrow+%5Cleft+%5C%7B+%7B%7B-18y%2By+%5E%7B2%7D+%2B16x%3D0%7D+%5Catop+%7B5y-8x%3D0%7D%7D+%5Cleft+%5C%7B+%7B%7B-18%5Ccdot+1%2C6x%2B%281%2C6x%29+%5E%7B2%7D+%2B16x%3D0%7D+%5Catop+%7By%3D1%2C6x%7D%7D)
Решаем первое уравнение:
-28,8х+2,56х²+16х=0
или
2,56х-12,8=0
х=5
у=1,6·5=8
Ответ
![\frac{5}{8}](https://tex.z-dn.net/?f=+%5Cfrac%7B5%7D%7B8%7D+)