SOLUTION: please help me express the following rational expressiond in lowest terms. 1) 4z/8z-12 2) y^5-3y^3+8y^2/5y 3) z^3+4z^2/z^2-8z+16 i am totally lost.any help would be gre

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: please help me express the following rational expressiond in lowest terms. 1) 4z/8z-12 2) y^5-3y^3+8y^2/5y 3) z^3+4z^2/z^2-8z+16 i am totally lost.any help would be gre      Log On


   

Question 166665: please help me express the following rational expressiond in lowest terms.
1) 4z/8z-12
2) y^5-3y^3+8y^2/5y
3) z^3+4z^2/z^2-8z+16
i am totally lost.any help would be great.
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 the GCF 4 from 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



%28y%5E5-3y%5E3%2B8y%5E2%29%2F%285y%29 Start with the given expression.


%28y%5E2%28y%5E3-3y%2B8%29%29%2F%285y%29 Factor the GCF y%5E2 from y%5E5-3y%5E3%2B8y%5E2 to get y%5E2%2A%28y%5E3-3%2Ay%2B8%29.


%28y%2Ay%28y%5E3-3y%2B8%29%29%2F%285y%29 Factor y%5E2 to get y%2Ay


%28y%2Ahighlight%28y%29%28y%5E3-3y%2B8%29%29%2F%285%2Ahighlight%28y%29%29 Highlight the common terms.


%28y%2Across%28y%29%28y%5E3-3y%2B8%29%29%2F%285%2Across%28y%29%29 Cancel out the common terms.


%28y%28y%5E3-3y%2B8%29%29%2F%285%29 Simplify


%28y%5E4-3y%5E2%2B8y%29%2F%285%29 Distribute


So %28y%5E5-3y%5E3%2B8y%5E2%29%2F%285y%29 simplifies to %28y%5E4-3y%5E2%2B8y%29%2F%285%29.


In other words, %28y%5E5-3y%5E3%2B8y%5E2%29%2F%285y%29=%28y%5E4-3y%5E2%2B8y%29%2F%285%29 where y%3C%3E0






# 3

Are you sure that the numerator is not z%5E3-4z%5E2 ???


%28z%5E3-4z%5E2%29%2F%28z%5E2-8z%2B16%29 Start with the given expression.


%28z%5E2%2A%28z-4%29%29%2F%28z%5E2-8z%2B16%29 Factor the GCF z%5E2 from z%5E3-4z%5E2 to get z%5E2%2A%28z-4%29.


%28z%5E2%2A%28z-4%29%29%2F%28%28z-4%29%28z-4%29%29 Factor z%5E2-8z%2B16 to get %28z-4%29%5E2.


%28z%5E2%2Ahighlight%28z-4%29%29%2F%28highlight%28z-4%29%28z-4%29%29 Highlight the common terms.


%28z%5E2%2Across%28z-4%29%29%2F%28cross%28z-4%29%28z-4%29%29 Cancel out the common terms.


%28z%5E2%29%2F%28z-4%29 Simplify.


So %28z%5E3-4z%5E2%29%2F%28z%5E2-8z%2B16%29 simplifies to %28z%5E2%29%2F%28z-4%29.


In other words, %28z%5E3-4z%5E2%29%2F%28z%5E2-8z%2B16%29=%28z%5E2%29%2F%28z-4%29 where z%3C%3E4