![1)\frac{4}{c+8} -\frac{12}{c^{2}+16c+64 }=\frac{4}{c+8}-\frac{12}{(c+8)^{2}}=\frac{4c+32-12}{(c+8)^{2}}=\frac{4c+20}{(c+8)^{2}}=\frac{4(c+5)}{(c+8)^{2}}\\\\2)\frac{c+5}{c^{2}-64}:\frac{4(c+5)}{(c+8)^{2}}=\frac{c+5}{(c+8)(c-8)}*\frac{(c+8)^{2}}{4(c+5)}=\frac{c+8}{4(c-8)}\\\\3)\frac{c+8}{4(c-8)}+\frac{4}{8-c}=\frac{c+8}{4(c-8)}-\frac{4}{c-8}=\frac{c+8-16}{4(c-8)}=\frac{c-8}{4(c-8)}=\frac{1}{4}=0,25](https://tex.z-dn.net/?f=1%29%5Cfrac%7B4%7D%7Bc%2B8%7D%20-%5Cfrac%7B12%7D%7Bc%5E%7B2%7D%2B16c%2B64%20%7D%3D%5Cfrac%7B4%7D%7Bc%2B8%7D-%5Cfrac%7B12%7D%7B%28c%2B8%29%5E%7B2%7D%7D%3D%5Cfrac%7B4c%2B32-12%7D%7B%28c%2B8%29%5E%7B2%7D%7D%3D%5Cfrac%7B4c%2B20%7D%7B%28c%2B8%29%5E%7B2%7D%7D%3D%5Cfrac%7B4%28c%2B5%29%7D%7B%28c%2B8%29%5E%7B2%7D%7D%5C%5C%5C%5C2%29%5Cfrac%7Bc%2B5%7D%7Bc%5E%7B2%7D-64%7D%3A%5Cfrac%7B4%28c%2B5%29%7D%7B%28c%2B8%29%5E%7B2%7D%7D%3D%5Cfrac%7Bc%2B5%7D%7B%28c%2B8%29%28c-8%29%7D%2A%5Cfrac%7B%28c%2B8%29%5E%7B2%7D%7D%7B4%28c%2B5%29%7D%3D%5Cfrac%7Bc%2B8%7D%7B4%28c-8%29%7D%5C%5C%5C%5C3%29%5Cfrac%7Bc%2B8%7D%7B4%28c-8%29%7D%2B%5Cfrac%7B4%7D%7B8-c%7D%3D%5Cfrac%7Bc%2B8%7D%7B4%28c-8%29%7D-%5Cfrac%7B4%7D%7Bc-8%7D%3D%5Cfrac%7Bc%2B8-16%7D%7B4%28c-8%29%7D%3D%5Cfrac%7Bc-8%7D%7B4%28c-8%29%7D%3D%5Cfrac%7B1%7D%7B4%7D%3D0%2C25)
В ответе получили число, значит значение выражения не зависит от входящей в него переменной.
![1)\frac{4}{x-7}+\frac{14}{x^{2}-14x+49}=\frac{4}{x-7}+\frac{14}{(x-7)^{2}}=\frac{4x-28+14}{(x-7)^{2}}=\frac{4x-14}{(x-7)^{2}}=\frac{2(2x-7)}{(x-7)^{2}}\\\\2)\frac{2(2x-7)}{(x-7)^{2} }*\frac{x^{2}-49 }{2x-7}=\frac{2(2x-7)(x-7)(x+7)}{(x-7)^{2}(2x-7)}=\frac{2x+14}{x-7}\\\\3)\frac{2x+14}{x-7} -\frac{7x-21}{x-7}=\frac{2x+14-7x+21}{x-7}=\frac{35-5x}{x-7}=\frac{5(7-x)}{x-7}=-5](https://tex.z-dn.net/?f=1%29%5Cfrac%7B4%7D%7Bx-7%7D%2B%5Cfrac%7B14%7D%7Bx%5E%7B2%7D-14x%2B49%7D%3D%5Cfrac%7B4%7D%7Bx-7%7D%2B%5Cfrac%7B14%7D%7B%28x-7%29%5E%7B2%7D%7D%3D%5Cfrac%7B4x-28%2B14%7D%7B%28x-7%29%5E%7B2%7D%7D%3D%5Cfrac%7B4x-14%7D%7B%28x-7%29%5E%7B2%7D%7D%3D%5Cfrac%7B2%282x-7%29%7D%7B%28x-7%29%5E%7B2%7D%7D%5C%5C%5C%5C2%29%5Cfrac%7B2%282x-7%29%7D%7B%28x-7%29%5E%7B2%7D%20%7D%2A%5Cfrac%7Bx%5E%7B2%7D-49%20%7D%7B2x-7%7D%3D%5Cfrac%7B2%282x-7%29%28x-7%29%28x%2B7%29%7D%7B%28x-7%29%5E%7B2%7D%282x-7%29%7D%3D%5Cfrac%7B2x%2B14%7D%7Bx-7%7D%5C%5C%5C%5C3%29%5Cfrac%7B2x%2B14%7D%7Bx-7%7D%20-%5Cfrac%7B7x-21%7D%7Bx-7%7D%3D%5Cfrac%7B2x%2B14-7x%2B21%7D%7Bx-7%7D%3D%5Cfrac%7B35-5x%7D%7Bx-7%7D%3D%5Cfrac%7B5%287-x%29%7D%7Bx-7%7D%3D-5)
Б
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
А) = 6(2х-у)
б) = 2b(a+3c)
в) = (n-3)(5m+2)
Ответ: Постаралась подробно расписать.
Объяснение: Будут вопросы обращайтесь.
![4^{x+1,5}+7*2^{x+1}=4\\(2^2)^{x+1,5}+7*2^{x+1}=4\\2^{2x+3}+7*2^{x+1}=4\\2^{2x}*2^3+7*2^x*2^1=4\\8*2^{2x}+14*2^x-4=0|:2\\a=2^x\\4a^2+7a-2=0\\D=7^2-4*4*(-2)=49+32=81=9^2\\a_1=1/4\\a_2=-2\\\2^x=1/4\\2^x=2^{-2}\\x=-2\\\\2^x\neq -2](https://tex.z-dn.net/?f=4%5E%7Bx%2B1%2C5%7D%2B7%2A2%5E%7Bx%2B1%7D%3D4%5C%5C%282%5E2%29%5E%7Bx%2B1%2C5%7D%2B7%2A2%5E%7Bx%2B1%7D%3D4%5C%5C2%5E%7B2x%2B3%7D%2B7%2A2%5E%7Bx%2B1%7D%3D4%5C%5C2%5E%7B2x%7D%2A2%5E3%2B7%2A2%5Ex%2A2%5E1%3D4%5C%5C8%2A2%5E%7B2x%7D%2B14%2A2%5Ex-4%3D0%7C%3A2%5C%5Ca%3D2%5Ex%5C%5C4a%5E2%2B7a-2%3D0%5C%5CD%3D7%5E2-4%2A4%2A%28-2%29%3D49%2B32%3D81%3D9%5E2%5C%5Ca_1%3D1%2F4%5C%5Ca_2%3D-2%5C%5C%5C2%5Ex%3D1%2F4%5C%5C2%5Ex%3D2%5E%7B-2%7D%5C%5Cx%3D-2%5C%5C%5C%5C2%5Ex%5Cneq+-2)
т.к. степень числа не может быть отрицательным числом
Ответ: -2