Answer:
![\frac{3x+4}{x^2-6x+5}=\frac{-7}{4(x-1)} +\frac{19}{4(x-5)}](https://tex.z-dn.net/?f=%5Cfrac%7B3x%2B4%7D%7Bx%5E2-6x%2B5%7D%3D%5Cfrac%7B-7%7D%7B4%28x-1%29%7D%20%2B%5Cfrac%7B19%7D%7B4%28x-5%29%7D)
Step-by-step explanation:
The given rational expression is:
![\frac{3x+4}{x^{2}-6x+5} = \frac{3x+4}{(x-1)(x-5)}](https://tex.z-dn.net/?f=%5Cfrac%7B3x%2B4%7D%7Bx%5E%7B2%7D-6x%2B5%7D%20%3D%20%5Cfrac%7B3x%2B4%7D%7B%28x-1%29%28x-5%29%7D)
We can use concept of Partial Fractions to solve this problem. Let,
![\frac{3x+4}{(x-1)(x-5)}=\frac{A}{x-1} +\frac{B}{x-5}](https://tex.z-dn.net/?f=%5Cfrac%7B3x%2B4%7D%7B%28x-1%29%28x-5%29%7D%3D%5Cfrac%7BA%7D%7Bx-1%7D%20%2B%5Cfrac%7BB%7D%7Bx-5%7D)
Multiplying both sides by (x - 1)(x - 5), we get:
![3x+4=A(x-5)+B(x-1)](https://tex.z-dn.net/?f=3x%2B4%3DA%28x-5%29%2BB%28x-1%29)
Substituting x = 5, we get:
![3(5)+4=A(5-5)+B(5-1)\\\\ 15+4=0+4B\\\\ 19=4B\\\\ B=\frac{19}{4}](https://tex.z-dn.net/?f=3%285%29%2B4%3DA%285-5%29%2BB%285-1%29%5C%5C%5C%5C%2015%2B4%3D0%2B4B%5C%5C%5C%5C%2019%3D4B%5C%5C%5C%5C%20B%3D%5Cfrac%7B19%7D%7B4%7D)
Substituting x = 1, we get:
![3(1)+4=A(1-5)+B(1-1)\\\\ 7=-4A\\\\ A=-\frac{7}{4}](https://tex.z-dn.net/?f=3%281%29%2B4%3DA%281-5%29%2BB%281-1%29%5C%5C%5C%5C%207%3D-4A%5C%5C%5C%5C%20A%3D-%5Cfrac%7B7%7D%7B4%7D)
Substituting the value of A and B, back in the original equation, we get:
![\frac{3x+4}{x^2-6x+5}=\frac{-7}{4(x-1)} +\frac{19}{4(x-5)}](https://tex.z-dn.net/?f=%5Cfrac%7B3x%2B4%7D%7Bx%5E2-6x%2B5%7D%3D%5Cfrac%7B-7%7D%7B4%28x-1%29%7D%20%2B%5Cfrac%7B19%7D%7B4%28x-5%29%7D)
Answer:
C. 1/2 divided by 13
Step-by-step explanation:
You have to divide the 1/2 gallon between the 13 people...not the 13 people by the 1/2 gallon! Can you mark brainliest again??
Hope it helps you! .........
You first identify what supplementary angles are,angles that add up to 180.
5x+2+8x+9=180
17x+11=180-11
17x=169
x=169divided by 17
x=9.9411
x=10 when rounded into the next value
8x*10=80+989