Start with
![\dfrac{2x-1}{2x+1}-\dfrac{2x+1}{2x-1}](https://tex.z-dn.net/?f=%5Cdfrac%7B2x-1%7D%7B2x%2B1%7D-%5Cdfrac%7B2x%2B1%7D%7B2x-1%7D)
Observe that this implies that the domain is
![2x+1,\ 2x-1\neq 0 \implies x \neq \pm\dfrac{1}{2}](https://tex.z-dn.net/?f=2x%2B1%2C%5C%202x-1%5Cneq%200%20%5Cimplies%20x%20%5Cneq%20%5Cpm%5Cdfrac%7B1%7D%7B2%7D)
The least common denominator is
![\dfrac{2x-1}{2x+1}-\dfrac{2x+1}{2x-1} = \dfrac{(2x-1)^2-(2x+1)^2}{(2x+1)(2x-1)}=\dfrac{-8x}{4x^2-1}](https://tex.z-dn.net/?f=%5Cdfrac%7B2x-1%7D%7B2x%2B1%7D-%5Cdfrac%7B2x%2B1%7D%7B2x-1%7D%20%3D%20%5Cdfrac%7B%282x-1%29%5E2-%282x%2B1%29%5E2%7D%7B%282x%2B1%29%282x-1%29%7D%3D%5Cdfrac%7B-8x%7D%7B4x%5E2-1%7D)
In the right hand side, we have
![-2\dfrac{2}{3}=-\left(2+\dfrac{2}[3}\right)=-\left(\dfrac{6}{3}+\dfrac{2}{3}\right)=-\dfrac{8}{3}](https://tex.z-dn.net/?f=-2%5Cdfrac%7B2%7D%7B3%7D%3D-%5Cleft%282%2B%5Cdfrac%7B2%7D%5B3%7D%5Cright%29%3D-%5Cleft%28%5Cdfrac%7B6%7D%7B3%7D%2B%5Cdfrac%7B2%7D%7B3%7D%5Cright%29%3D-%5Cdfrac%7B8%7D%7B3%7D)
So, the equation becomes
![-\dfrac{8x}{4x^2-1}=-\dfrac{8}{3} \iff \dfrac{x}{4x^2-1}=\dfrac{1}{3}](https://tex.z-dn.net/?f=-%5Cdfrac%7B8x%7D%7B4x%5E2-1%7D%3D-%5Cdfrac%7B8%7D%7B3%7D%20%5Ciff%20%5Cdfrac%7Bx%7D%7B4x%5E2-1%7D%3D%5Cdfrac%7B1%7D%7B3%7D)
Multiply both sides by 3:
![\dfrac{3x}{4x^2-1}=1 \iff 3x=4x^2-1 \iff 4x^2-3x-1=0](https://tex.z-dn.net/?f=%5Cdfrac%7B3x%7D%7B4x%5E2-1%7D%3D1%20%5Ciff%203x%3D4x%5E2-1%20%5Ciff%204x%5E2-3x-1%3D0)
This equation has solutions
![x=-\dfrac{1}{4},\quad x=1](https://tex.z-dn.net/?f=x%3D-%5Cdfrac%7B1%7D%7B4%7D%2C%5Cquad%20x%3D1)
Which are compliant with the domain of the equation
For 4(3x-1) = 24 -> 3x-1 = 6 -> x = 7/3
For 12x-1 = 24 -> x = 12/25
Apparently, the solution is not the same.
They always try to trick you with this. Remember anything 5 or above would round up, anything 4 and under would round down. So look for the tenth place. that's the 9. The number to the right is 8 which is greater than 5. That means round up. You can't round it to 0.1 because that takes it back down. So you just move it over. The answer is 1.0.
Answer:
food bill, electric bill
Step-by-step explanation:
Variable expenses change every money
Loan payments are usually fixed, the same every month
food bill - variable expense since you buy different food each month and they will cost different amounts
rent is a fixed expense
the electric bill is different every month because some months you use more electricity than others
Answer:
Salma can run 1 to 8 more miles to run less than 28 miles in total
Step-by-step explanation:
28-19= 9 but she is running LESS than 28 miles so subtract 1 from that 9