SOLUTION: i dont really understand this either really; x^2-9/x-2 * x^2-4/x-3 i think i solved it totally wrong since i first multiplied the top then the bottom and got x^4 - 13x^2 +36 / x^2

Algebra ->  Numeric Fractions Calculators, Lesson and Practice -> SOLUTION: i dont really understand this either really; x^2-9/x-2 * x^2-4/x-3 i think i solved it totally wrong since i first multiplied the top then the bottom and got x^4 - 13x^2 +36 / x^2      Log On


   

Question 144816: i dont really understand this either really; x^2-9/x-2 * x^2-4/x-3
i think i solved it totally wrong since i first multiplied the top then the bottom and got x^4 - 13x^2 +36 / x^2 - x - 6.
could someone please show me how to solve it right?
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
%28%28x%5E2-9%29%2F%28x-2%29%29%28%28x%5E2-4%29%2F%28x-3%29%29

Both of the numerators are the difference of two squares, so factor them:

%28%28x%2B3%29%28x-3%29%2F%28x-2%29%29%28%28x%2B2%29%28x-2%29%2F%28x-3%29%29

Multiply numerators and denominators, just like you would any other fractions:

%28%28x%2B3%29%28x-3%29%28x%2B2%29%28x-2%29%29%2F%28%28x-2%29%28x-3%29%29

Eliminate factors common to both numerator and denominator because a%2Fa=1 for all real a:



And that's really how it works, really. Commit that "difference of two squares" factorization pattern to memory, you will see it and need to use it many times before you have completed all of your math education.