Answer: The expression is undefined for x=4 and x=5.
The expression is undefined for any x that makes the denominator 0. This leads to solving a quadratic equation:
![\frac{x+3}{x^2-9x+20}\\x^2-9x+20\neq 0\\x_{1,2}\neq\frac{9\pm\sqrt{9^2-80}}{2}=\frac{9\pm1}{2}\\x_1\neq4\\x_2\neq5](https://tex.z-dn.net/?f=%5Cfrac%7Bx%2B3%7D%7Bx%5E2-9x%2B20%7D%5C%5Cx%5E2-9x%2B20%5Cneq%200%5C%5Cx_%7B1%2C2%7D%5Cneq%5Cfrac%7B9%5Cpm%5Csqrt%7B9%5E2-80%7D%7D%7B2%7D%3D%5Cfrac%7B9%5Cpm1%7D%7B2%7D%5C%5Cx_1%5Cneq4%5C%5Cx_2%5Cneq5)
p=1
Step-by-step explanation:
![3p + 7 = - 4(4 - 6p) + 2 \\ 3p + 7 = - 16 + 24p + 2 \\ 3p - 24p = - 16 + 2 - 7 \\ - 21p = - 21](https://tex.z-dn.net/?f=3p%20%2B%207%20%3D%20%20-%204%284%20-%206p%29%20%2B%202%20%5C%5C%203p%20%2B%207%20%3D%20%20-%2016%20%2B%2024p%20%2B%202%20%5C%5C%203p%20-%2024p%20%3D%20%20-%2016%20%2B%202%20-%207%20%5C%5C%20%20-%2021p%20%3D%20%20-%2021)
![\frac{ - 21p}{ - 21} = \frac{ - 21}{ - 21} \\ p = 1](https://tex.z-dn.net/?f=%20%5Cfrac%7B%20-%2021p%7D%7B%20-%2021%7D%20%20%3D%20%20%5Cfrac%7B%20-%2021%7D%7B%20-%2021%7D%20%20%5C%5C%20p%20%3D%201)
Answer:
![-p^2+32](https://tex.z-dn.net/?f=-p%5E2%2B32)
Step-by-step explanation:
Start by expanding the
into the
bracket using the distributive method:
![-2(p-4)\\-2p + 8](https://tex.z-dn.net/?f=-2%28p-4%29%5C%5C-2p%20%2B%208)
Now, expand the result into the remaining bracket:
![(-2p + 8)(p+4)\\-2p^2 -8p+8p+32\\-2p^2 + 32](https://tex.z-dn.net/?f=%28-2p%20%2B%208%29%28p%2B4%29%5C%5C-2p%5E2%20-8p%2B8p%2B32%5C%5C-2p%5E2%20%2B%2032)
The square root of four is two
2x2 + 8x - 12 = 0
4 + 8x - 12 = 0
8x = 12 - 4
8x = 8
x = 1