Answer:
x =1, x = 0 is extraneous.
Step-by-step explanation:
5/x = 4x + 1 / x^2
5x^2 = 4x^2 + x
5x^2 - 4x^2 - x = 0
x^2 - x = 0
x(x - 1) = 0
x = 0, 1.
x is not a solution because 5/x is undefined.
Answer:
The answer to this question can be defined as follows:
In part (i), the answer is "option d".
In part (ii), the answer is "option 2".
Step-by-step explanation:
Given:
Part (a)
![\Rightarrow \bold{\frac{x^2+x-20}{x-4}=x+5}\\\\](https://tex.z-dn.net/?f=%5CRightarrow%20%5Cbold%7B%5Cfrac%7Bx%5E2%2Bx-20%7D%7Bx-4%7D%3Dx%2B5%7D%5C%5C%5C%5C)
Solve the above equation:
![\Rightarrow x^2+x-20=(x+5)(x-4)\\\\\Rightarrow x^2+x-20=(x^2-4x+5x-20)\\\\\Rightarrow x^2+x-20=x^2-4x+5x-20\\\\\Rightarrow \boxed{x^2+x-20=x^2+x-20}\\](https://tex.z-dn.net/?f=%5CRightarrow%20x%5E2%2Bx-20%3D%28x%2B5%29%28x-4%29%5C%5C%5C%5C%5CRightarrow%20x%5E2%2Bx-20%3D%28x%5E2-4x%2B5x-20%29%5C%5C%5C%5C%5CRightarrow%20x%5E2%2Bx-20%3Dx%5E2-4x%2B5x-20%5C%5C%5C%5C%5CRightarrow%20%5Cboxed%7Bx%5E2%2Bx-20%3Dx%5E2%2Bx-20%7D%5C%5C)
Given:
Part (b)
![\Rightarrow \bold{ \lim_{x \to \3} \frac{x^2+x-12}{x-3}= \lim_{x \to 3} (x+4)}\\\\](https://tex.z-dn.net/?f=%5CRightarrow%20%5Cbold%7B%20%5Clim_%7Bx%20%5Cto%20%5C3%7D%20%5Cfrac%7Bx%5E2%2Bx-12%7D%7Bx-3%7D%3D%20%5Clim_%7Bx%20%5Cto%203%7D%20%28x%2B4%29%7D%5C%5C%5C%5C)
Solve the above equation:
factor of ![\Rightarrow x^2+x-20 =(x-3)(x+4)](https://tex.z-dn.net/?f=%5CRightarrow%20x%5E2%2Bx-20%20%3D%28x-3%29%28x%2B4%29)
![\Rightarrow \lim_{x \to \3} \frac{(x-3)(x+4)}{x-3}= \lim_{x \to 3} (x+4)\\\\\Rightarrow \lim_{x \to \3} (x+4)= \lim_{x \to 3} (x+4)\\\\](https://tex.z-dn.net/?f=%5CRightarrow%20%20%5Clim_%7Bx%20%5Cto%20%5C3%7D%20%5Cfrac%7B%28x-3%29%28x%2B4%29%7D%7Bx-3%7D%3D%20%5Clim_%7Bx%20%5Cto%203%7D%20%28x%2B4%29%5C%5C%5C%5C%5CRightarrow%20%20%5Clim_%7Bx%20%5Cto%20%5C3%7D%20%28x%2B4%29%3D%20%5Clim_%7Bx%20%5Cto%203%7D%20%28x%2B4%29%5C%5C%5C%5C)
apply limit value:
![\Rightarrow (3+4)= (3+4)\\\\\Rightarrow 7= 7](https://tex.z-dn.net/?f=%5CRightarrow%20%20%283%2B4%29%3D%20%20%283%2B4%29%5C%5C%5C%5C%5CRightarrow%20%207%3D%207)
Answer:
The first one is incorrect
Step-by-step explanation:
3^2 - 5 + 2
9 - 5 + 2
4+2 = 6 (not 42)
Answer:
acircle has infintely many axes of symmetry
Step-by-step explanation: