SOLUTION: please help me express the following rational expressions in lowest terms. 1) y^2-y-12/y^2-9 2) 3x^2-6x-72/2x^2-8x-64 i am totally lost. any help would be great.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: please help me express the following rational expressions in lowest terms. 1) y^2-y-12/y^2-9 2) 3x^2-6x-72/2x^2-8x-64 i am totally lost. any help would be great.      Log On


   

Question 166667: please help me express the following rational expressions in lowest terms.
1) y^2-y-12/y^2-9
2) 3x^2-6x-72/2x^2-8x-64

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!
The key to these type of problems is factoring.


# 1


%28y%5E2-y-12%29%2F%28y%5E2-9%29 Start with the given expression.


%28%28y%2B3%29%28y-4%29%29%2F%28y%5E2-9%29 Factor y%5E2-y-12 to get %28y%2B3%29%2A%28y-4%29.


%28%28y%2B3%29%28y-4%29%29%2F%28%28y-3%29%28y%2B3%29%29 Factor y%5E2-9 to get %28y-3%29%2A%28y%2B3%29.


%28highlight%28%28y%2B3%29%29%28y-4%29%29%2F%28%28y-3%29highlight%28%28y%2B3%29%29%29 Highlight the common terms.


%28cross%28%28y%2B3%29%29%28y-4%29%29%2F%28%28y-3%29cross%28%28y%2B3%29%29%29 Cancel out the common terms.


%28y-4%29%2F%28y-3%29 Simplify.


So %28y%5E2-y-12%29%2F%28y%5E2-9%29 simplifies to %28y-4%29%2F%28y-3%29.


In other words, %28y%5E2-y-12%29%2F%28y%5E2-9%29=%28%28y-4%29%29%2F%28%28y-3%29%29 where y%3C%3E3 or y%3C%3E-3






# 2


%283x%5E2-6x-72%29%2F%282x%5E2-8x-64%29 Start with the given expression.


%283%28x%2B4%29%28x-6%29%29%2F%282x%5E2-8x-64%29 Factor 3x%5E2-6x-72 to get 3%2A%28x%2B4%29%2A%28x-6%29.


%283%28x%2B4%29%28x-6%29%29%2F%282%28x%2B4%29%28x-8%29%29 Factor 2x%5E2-8x-64 to get 2%2A%28x%2B4%29%2A%28x-8%29.


Highlight the common terms.


%28%283%29cross%28%28x%2B4%29%29%28x-6%29%29%2F%28%282%29cross%28%28x%2B4%29%29%28x-8%29%29 Cancel out the common terms.


%283%28x-6%29%29%2F%282%28x-8%29%29 Simplify.


%283x-18%29%2F%282x-16%29 Distribute


So %283x%5E2-6x-72%29%2F%282x%5E2-8x-64%29 simplifies to %283x-18%29%2F%282x-16%29.


In other words, %283x%5E2-6x-72%29%2F%282x%5E2-8x-64%29=%283x-18%29%2F%282x-16%29 where x%3C%3E-4 or x%3C%3E8