$6.80 dollars for the item if it is marked down by 15%
Answer:
x = 4
Step-by-step explanation:
2x - 1 = 7
2x = 7 + 1
2x = 8
x = 8/2
x = 4
Answer:
![\frac{x^2-4}{x+2} = x-2\\\frac{4x^2-1}{2x+1} = 2x-1](https://tex.z-dn.net/?f=%5Cfrac%7Bx%5E2-4%7D%7Bx%2B2%7D%20%3D%20x-2%5C%5C%5Cfrac%7B4x%5E2-1%7D%7B2x%2B1%7D%20%3D%202x-1)
Step-by-step explanation:
<u>a) (x2 - 4)/(x + 2)</u>
We can simply use factorization to solve the given question.
Here the first term will be numerator and second term will be denominator.
We will factorize the numerator.
So,
![\frac{x^2-4}{x+2}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%5E2-4%7D%7Bx%2B2%7D)
Using formula, ![a^2+b^2 = (a+b)(a-b)](https://tex.z-dn.net/?f=a%5E2%2Bb%5E2%20%3D%20%28a%2Bb%29%28a-b%29)
![\frac{x^2-4}{x+2}\\= \frac{(x^2)-(2)^2}{x+2}\\=\frac{(x+2)(x-2)}{x+2}\\= x-2](https://tex.z-dn.net/?f=%5Cfrac%7Bx%5E2-4%7D%7Bx%2B2%7D%5C%5C%3D%20%5Cfrac%7B%28x%5E2%29-%282%29%5E2%7D%7Bx%2B2%7D%5C%5C%3D%5Cfrac%7B%28x%2B2%29%28x-2%29%7D%7Bx%2B2%7D%5C%5C%3D%20x-2)
<u>b) (4x2 - 1) / (2x + 1)</u>
We can simply use factorization to solve the given question.
Here the first term will be numerator and second term will be denominator.
We will factorize the numerator.
![\frac{4x^2-1}{2x+1}](https://tex.z-dn.net/?f=%5Cfrac%7B4x%5E2-1%7D%7B2x%2B1%7D)
Using formula, ![a^2+b^2 = (a+b)(a-b)](https://tex.z-dn.net/?f=a%5E2%2Bb%5E2%20%3D%20%28a%2Bb%29%28a-b%29)
![= \frac{(2x)^2-(1)^2}{2x+1}\\=\frac{(2x+1)(2x-1)}{2x+1}\\= 2x-1](https://tex.z-dn.net/?f=%3D%20%5Cfrac%7B%282x%29%5E2-%281%29%5E2%7D%7B2x%2B1%7D%5C%5C%3D%5Cfrac%7B%282x%2B1%29%282x-1%29%7D%7B2x%2B1%7D%5C%5C%3D%202x-1)
Hence,
![\frac{x^2-4}{x+2} = x-2\\\frac{4x^2-1}{2x+1} = 2x-1](https://tex.z-dn.net/?f=%5Cfrac%7Bx%5E2-4%7D%7Bx%2B2%7D%20%3D%20x-2%5C%5C%5Cfrac%7B4x%5E2-1%7D%7B2x%2B1%7D%20%3D%202x-1)