8/28=4/14=2/7
2/7 is simplest form
Not 100% sure but hopefully this helps
It follows from the definition of the binomial coefficient:
![\dbinom nr=\dfrac{n!}{r!(n-r)!}](https://tex.z-dn.net/?f=%5Cdbinom%20nr%3D%5Cdfrac%7Bn%21%7D%7Br%21%28n-r%29%21%7D)
So we have
![(n+1)\dbinom nr=(n+1)\dfrac{n!}{r!(n-r)!}=(r+1)\dfrac{(n+1)!}{(r+1)!(n-r)!}](https://tex.z-dn.net/?f=%28n%2B1%29%5Cdbinom%20nr%3D%28n%2B1%29%5Cdfrac%7Bn%21%7D%7Br%21%28n-r%29%21%7D%3D%28r%2B1%29%5Cdfrac%7B%28n%2B1%29%21%7D%7B%28r%2B1%29%21%28n-r%29%21%7D)
That is,
gets absorbed into the numerator's factorial, and we introduct
into the denominator. Now,
, so we get
![(n+1)\dbinom nr=(r+1)\dfrac{(n+1)!}{(r+1)!((n+1)-(r+1))!}=(r+1)\dbinom{n+1}{r+1}](https://tex.z-dn.net/?f=%28n%2B1%29%5Cdbinom%20nr%3D%28r%2B1%29%5Cdfrac%7B%28n%2B1%29%21%7D%7B%28r%2B1%29%21%28%28n%2B1%29-%28r%2B1%29%29%21%7D%3D%28r%2B1%29%5Cdbinom%7Bn%2B1%7D%7Br%2B1%7D)
as required.
Answer:
3x³+3x²+3x+8+![\frac{4}{x-1}](https://tex.z-dn.net/?f=%5Cfrac%7B4%7D%7Bx-1%7D)
Step-by-step explanation:
You can use synthetic division for this problem since the divisor is in (x-a) form. The fraction is the remainder over the divisor.
2y=-8
We need to clear "y" with inverse operations.
y= -8/2 if 2 was multiplying now is dividing
y= -4