SOLUTION: My teacher gave this problem 4x^-9 ------ 4x^2+12x+9 divided by 6x-9 I got 3(2x+3), my teacher said I was wrong.Please help me.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: My teacher gave this problem 4x^-9 ------ 4x^2+12x+9 divided by 6x-9 I got 3(2x+3), my teacher said I was wrong.Please help me.      Log On


   

Question 156524: My teacher gave this problem
4x^-9
------
4x^2+12x+9 divided by 6x-9
I got 3(2x+3), my teacher said I was wrong.Please help me.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Is the expression %28%284x%5E2-9%29%2F%284x%5E2%2B12x%2B9%29%29%2F%286x-9%29 ???


%28%284x%5E2-9%29%2F%284x%5E2%2B12x%2B9%29%29%2F%286x-9%29 Start with the given expression



%28%284x%5E2-9%29%2F%284x%5E2%2B12x%2B9%29%29%2F%28%286x-9%29%2F1%29 Rewrite 6x-9 as %286x-9%29%2F1



%28%284x%5E2-9%29%2F%284x%5E2%2B12x%2B9%29%29%2A%281%2F%286x-9%29%29 Multiply the first fraction %284x%5E2-9%29%2F%284x%5E2%2B12x%2B9%29 by the reciprocal of the second fraction %286x-9%29%2F1



%28%28%282x%2B3%29%282x-3%29%29%2F%284x%5E2%2B12x%2B9%29%29%2A%281%2F%286x-9%29%29 Factor 4x%5E2-9 to get %282x%2B3%29%282x-3%29



%28%28%282x%2B3%29%282x-3%29%29%2F%28%282x%2B3%29%282x%2B3%29%29%29%2A%281%2F%286x-9%29%29 Factor 4x%5E2%2B12x%2B9 to get %282x%2B3%29%282x%2B3%29


Factor 6x-9 to get 3%282x-3%29



%28%282x%2B3%29%282x-3%29%29%2F%283%282x%2B3%29%282x%2B3%29%282x-3%29%29 Combine the fractions.



Highlight the common terms.


Cancel out the common terms.


1%2F%283%282x%2B3%29%29 Simplify


1%2F%286x%2B9%29 Distribute (this step is optional)


So %28%284x%5E2-9%29%2F%284x%5E2%2B12x%2B9%29%29%2F%286x-9%29 simplifies to 1%2F%283%282x%2B3%29%29 (which is the same as 1%2F%286x%2B9%29)




Note: you can use a graph to verify your answer. Simply graph the original expression and the answer. If the two graphs are identical (which in this case they are), then this shows that the two expressions are equivalent and it verifies the answer.