Answer: -1
Step-by-step explanation: To evaluate this problem, the first thing we want to do is plug in the appropriate value for <em>x</em>.
When we do that, we get ![\frac{(-2)^2- 8}{-2 + 6}](https://tex.z-dn.net/?f=%5Cfrac%7B%28-2%29%5E2-%208%7D%7B-2%20%2B%206%7D)
A good rule of thumb for problems that involve division bars is to simplify what's above the division bar as much as you can and what's below the division bar as much as you can before you do your dividing.
So up top if we follow our order of operations, the first thing we want to do is square the -2 before we subtract. So -2² is +4.
So in our numerator we have 4 - 8.
Down below, we have -2 + 6 which is +4.
4 - 8 is -4 and -2 + 6 is +4.
![-1.](https://tex.z-dn.net/?f=-1.)
Answer:
B
Step-by-step explanation:
840÷8=105
Answer:
252 songs per 18 CD's
252/18 = 14
14 songs per CD
Step-by-step explanation:
When you add something, you gain more of it. Therefore, it should be positive 2
2
Answer:
![\frac{3}{x + 3} + \frac{2}{(x+3)^2}](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7Bx%20%2B%203%7D%20%2B%20%5Cfrac%7B2%7D%7B%28x%2B3%29%5E2%7D)
Step-by-step explanation:
Given
![\frac{3x + 11}{x^2 +6x + 9}](https://tex.z-dn.net/?f=%5Cfrac%7B3x%20%2B%2011%7D%7Bx%5E2%20%2B6x%20%2B%209%7D)
Required
Express as partial fraction
![\frac{3x + 11}{x^2 +6x + 9}](https://tex.z-dn.net/?f=%5Cfrac%7B3x%20%2B%2011%7D%7Bx%5E2%20%2B6x%20%2B%209%7D)
Expand the numerator
![\frac{3x + 11}{x^2 +3x +3x+ 9}](https://tex.z-dn.net/?f=%5Cfrac%7B3x%20%2B%2011%7D%7Bx%5E2%20%2B3x%20%2B3x%2B%209%7D)
Factorize
![\frac{3x + 11}{x(x +3) +3(x+ 3)}](https://tex.z-dn.net/?f=%5Cfrac%7B3x%20%2B%2011%7D%7Bx%28x%20%2B3%29%20%2B3%28x%2B%203%29%7D)
Factor out x + 3
![\frac{3x + 11}{(x +3)(x+ 3)}](https://tex.z-dn.net/?f=%5Cfrac%7B3x%20%2B%2011%7D%7B%28x%20%2B3%29%28x%2B%203%29%7D)
![\frac{3x + 11}{(x +3)^2}](https://tex.z-dn.net/?f=%5Cfrac%7B3x%20%2B%2011%7D%7B%28x%20%2B3%29%5E2%7D)
As a partial fraction, we have:
![\frac{3x + 11}{(x +3)^2} = \frac{A}{x + 3} + \frac{B}{(x+3)^2}](https://tex.z-dn.net/?f=%5Cfrac%7B3x%20%2B%2011%7D%7B%28x%20%2B3%29%5E2%7D%20%3D%20%5Cfrac%7BA%7D%7Bx%20%2B%203%7D%20%2B%20%5Cfrac%7BB%7D%7B%28x%2B3%29%5E2%7D)
Take LCM
![\frac{3x + 11}{(x +3)^2} = \frac{A(x+3) + B}{(x + 3)^2}](https://tex.z-dn.net/?f=%5Cfrac%7B3x%20%2B%2011%7D%7B%28x%20%2B3%29%5E2%7D%20%3D%20%5Cfrac%7BA%28x%2B3%29%20%2B%20B%7D%7B%28x%20%2B%203%29%5E2%7D)
Cancel out (x + 3)^2 on both sides
![3x + 11 = A(x+3) + B](https://tex.z-dn.net/?f=3x%20%2B%2011%20%3D%20A%28x%2B3%29%20%2B%20B)
Open bracket
![3x + 11 = Ax+3A + B](https://tex.z-dn.net/?f=3x%20%2B%2011%20%3D%20Ax%2B3A%20%2B%20B)
By comparison, we have:
===> ![A = 3](https://tex.z-dn.net/?f=A%20%3D%203)
![3A + B = 11](https://tex.z-dn.net/?f=3A%20%2B%20B%20%3D%2011)
Substitute 3 for A
![3*3 + B = 11](https://tex.z-dn.net/?f=3%2A3%20%2B%20B%20%3D%2011)
![9 + B = 11](https://tex.z-dn.net/?f=9%20%2B%20B%20%3D%2011)
Solve for B
![B = 11-9](https://tex.z-dn.net/?f=B%20%3D%2011-9)
![B =2](https://tex.z-dn.net/?f=B%20%3D2)
Substitute:
and
in
![\frac{3x + 11}{(x +3)^2} = \frac{A}{x + 3} + \frac{B}{(x+3)^2}](https://tex.z-dn.net/?f=%5Cfrac%7B3x%20%2B%2011%7D%7B%28x%20%2B3%29%5E2%7D%20%3D%20%5Cfrac%7BA%7D%7Bx%20%2B%203%7D%20%2B%20%5Cfrac%7BB%7D%7B%28x%2B3%29%5E2%7D)
![\frac{3x + 11}{(x +3)^2} = \frac{3}{x + 3} + \frac{2}{(x+3)^2}](https://tex.z-dn.net/?f=%5Cfrac%7B3x%20%2B%2011%7D%7B%28x%20%2B3%29%5E2%7D%20%3D%20%5Cfrac%7B3%7D%7Bx%20%2B%203%7D%20%2B%20%5Cfrac%7B2%7D%7B%28x%2B3%29%5E2%7D)
Hence, the partial fraction is:
![\frac{3}{x + 3} + \frac{2}{(x+3)^2}](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7Bx%20%2B%203%7D%20%2B%20%5Cfrac%7B2%7D%7B%28x%2B3%29%5E2%7D)