SOLUTION: Please help 1.) 4z __________ 8z-12 2.) z^3+4z^2

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Please help 1.) 4z __________ 8z-12 2.) z^3+4z^2       Log On


   

Question 154268: Please help

1.) 4z
__________
8z-12

2.) z^3+4z^2
---------
z^2+8z+16
lowest term
Thank you for helping
Found 2 solutions by checkley77, jim_thompson5910:
Answer by checkley77(12844) About Me  (Show Source):
You can put this solution on YOUR website!
1.) 4z
__________ =4z/4(2z-3)=z/(2z-3)

8z-12
2). z^3+4z^2
----------- = (z^2)(z+4)/(z+4)(z+4)=z^2/(x+4)
z^2+8z+16

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
# 1

%284z%29%2F%288z-12%29 Start with the given expression.


%284z%29%2F%284%282z-3%29%29 Factor 8z-12 to get 4%282z-3%29.


%28highlight%284%29z%29%2F%28highlight%284%29%282z-3%29%29 Highlight the common terms.


%28cross%284%29z%29%2F%28cross%284%29%282z-3%29%29 Cancel out the common terms.


%28z%29%2F%282z-3%29 Simplify.


So %284z%29%2F%288z-12%29 simplifies to %28z%29%2F%282z-3%29.


In other words, %284z%29%2F%288z-12%29=%28z%29%2F%282z-3%29 where z%3C%3E3%2F2




# 2



%28z%5E3%2B4z%5E2%29%2F%28z%5E2%2B8z%2B16%29 Start with the given expression.


%28z%5E2%2A%28z%2B4%29%29%2F%28z%5E2%2B8z%2B16%29 Factor z%5E3%2B4z%5E2 to get z%5E2%2A%28z%2B4%29.


%28z%5E2%2A%28z%2B4%29%29%2F%28%28z%2B4%29%28z%2B4%29%29 Factor z%5E2%2B8z%2B16 to get %28z%2B4%29%28z%2B4%29.


%28z%5E2highlight%28%28z%2B4%29%29%29%2F%28highlight%28%28z%2B4%29%29%28z%2B4%29%29 Highlight the common terms.


%28z%5E2cross%28%28z%2B4%29%29%29%2F%28cross%28%28z%2B4%29%29%28z%2B4%29%29 Cancel out the common terms.


%28z%5E2%29%2F%28z%2B4%29 Simplify.


So %28z%5E3%2B4z%5E2%29%2F%28z%5E2%2B8z%2B16%29 simplifies to %28z%5E2%29%2F%28z%2B4%29.


In other words, %28z%5E3%2B4z%5E2%29%2F%28z%5E2%2B8z%2B16%29=%28z%5E2%29%2F%28z%2B4%29 where z%3C%3E-4