SOLUTION: Please help lowest term 1. 24x^3/6y^2 divided by 8xz^4/3y^4 2. z^2-10z+21/z^2-13z+36 divided by z^2-11z+24/z^2-9z+14

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Please help lowest term 1. 24x^3/6y^2 divided by 8xz^4/3y^4 2. z^2-10z+21/z^2-13z+36 divided by z^2-11z+24/z^2-9z+14       Log On


   

Question 154270: Please help
lowest term
1. 24x^3/6y^2 divided by 8xz^4/3y^4

2. z^2-10z+21/z^2-13z+36 divided by z^2-11z+24/z^2-9z+14
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
# 1

%28%2824x%5E3%29%2F%286y%5E2%29%29%2F%28%288xz%5E4%29%2F%283y%5E4%29%29 Start with the given expression


%28%2824x%5E3%29%2F%286y%5E2%29%29%2A%28%283y%5E4%29%2F%288xz%5E4%29%29 Multiply the first fraction by the reciprocal of the second fraction.


%28%2824x%5E3%29%283y%5E4%29%29%2F%28%286y%5E2%29%288xz%5E4%29%29 Combine the fractions.


%2872x%5E3y%5E4%29%2F%2848xy%5E2z%5E4%29 Multiply


%2824%2A3%2Ax%2Ax%2Ax%2Ay%2Ay%2Ay%2Ay%29%2F%2824%2A2%2Ax%2Ay%2Ay%2Az%2Az%2Az%2Az%29 Factor. In this case, 72x%5E3y%5E4=24%2A3%2Ax%2Ax%2Ax%2Ay%2Ay%2Ay%2Ay and 48xy%5E2z%5E4=24%2A2%2Ax%2Ay%2Ay%2Az%2Az%2Az%2Az


Highlight the common terms.


Cancel out the common terms.


%283%2Ax%2Ax%2Ay%2Ay%29%2F%282%2Az%2Az%2Az%2Az%29 Simplify.


%283%2Ax%5E2%2Ay%5E2%29%2F%282%2Az%5E4%29 Regroup.


So %2872x%5E3y%5E4%29%2F%2848xy%5E2z%5E4%29 simplifies to %283%2Ax%5E2%2Ay%5E2%29%2F%282%2Az%5E4%29.


In other words, %2872x%5E3y%5E4%29%2F%2848xy%5E2z%5E4%29=%283%2Ax%5E2%2Ay%5E2%29%2F%282%2Az%5E4%29 where x%3C%3E0, y%3C%3E0, and z%3C%3E0




# 2



Start with the given expression.


Multiply the first fraction %28z%5E2-10z%2B21%29%2F%28z%5E2-13z%2B36%29 by the reciprocal of the second fraction %28z%5E2-11z%2B24%29%2F%28z%5E2-9z%2B14%29.


Factor z%5E2-10z%2B21 to get %28z-3%29%2A%28z-7%29.


Factor z%5E2-13z%2B36 to get %28z-4%29%2A%28z-9%29.


Factor z%5E2-9z%2B14 to get %28z-2%29%2A%28z-7%29.


Factor z%5E2-11z%2B24 to get %28z-3%29%2A%28z-8%29.


Combine the fractions.


Highlight the common terms.


Cancel out the common terms.


%28%28z-7%29%28z-2%29%28z-7%29%29%2F%28%28z-4%29%28z-9%29%28z-8%29%29 Simplify.


%28%28z-2%29%28z-7%29%5E2%29%2F%28%28z-4%29%28z-9%29%28z-8%29%29 Regroup the terms.


So simplifies to %28%28z-2%29%28z-7%29%5E2%29%2F%28%28z-4%29%28z-9%29%28z-8%29%29.


In other words, where z%3C%3E3, z%3C%3E4, z%3C%3E8, or z%3C%3E9