SOLUTION: I have tired everything to solve this problem x 3 3 ________ + ________ + _______ x^2 - 9 x^2+6x+9 6 - 2x Any help. Thank you

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: I have tired everything to solve this problem x 3 3 ________ + ________ + _______ x^2 - 9 x^2+6x+9 6 - 2x Any help. Thank you      Log On


   

Question 172179This question is from textbook Functions and Algebraic Methods
: I have tired everything to solve this problem
x 3 3
________ + ________ + _______
x^2 - 9 x^2+6x+9 6 - 2x
Any help. Thank you so much!



This question is from textbook Functions and Algebraic Methods

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
x%2F%28x%5E2-9%29%2B3%2F%28x%5E2%2B6x%2B9%29%2B3%2F%286-2x%29 Start with the given expression


x%2F%28%28x%2B3%29%28x-3%29%29%2B3%2F%28x%5E2%2B6x%2B9%29%2B3%2F%286-2x%29 Factor x%5E2-9 to get %28x%2B3%29%28x-3%29


x%2F%28%28x%2B3%29%28x-3%29%29%2B3%2F%28%28x%2B3%29%28x%2B3%29%29%2B3%2F%286-2x%29 Factor x%5E2%2B6x%2B9 to get %28x%2B3%29%28x%2B3%29


x%2F%28%28x%2B3%29%28x-3%29%29%2B3%2F%28%28x%2B3%29%28x%2B3%29%29%2B3%2F%28-2%28x-3%29%29 Factor 6-2x to get 2%283-x%29=-2%28x-3%29



x%2F%28%28x%2B3%29%28x-3%29%29%2B3%2F%28%28x%2B3%29%28x%2B3%29%29-3%2F%282%28x-3%29%29 Reduce



Take note that the LCD is 2%28x%2B3%29%28x%2B3%29%28x-3%29. So the goal is to get EVERY denominator equal to the LCD


Multiply the first fraction by %282%28x%2B3%29%29%2F%282%28x%2B3%29%29


Multiply the second fraction by %282%28x-3%29%29%2F%282%28x-3%29%29


Multiply the third fraction by %28%28x%2B3%29%28x%2B3%29%29%2F%28%28x%2B3%29%28x%2B3%29%29


FOIL


Distribute


Combine the fractions.


%282x%5E2%2B6x%2B6x-18-3x%5E2-18x-27%29%2F%282%28x%2B3%29%28x%2B3%29%28x-3%29%29 Distribute


%28-x%5E2-6x-45%29%2F%282%28x%2B3%29%28x%2B3%29%28x-3%29%29 Combine like terms.


So x%2F%28x%5E2-9%29%2B3%2F%28x%5E2%2B6x%2B9%29%2B3%2F%286-2x%29 combines and simplifies to %28-x%5E2-6x-45%29%2F%282%28x%2B3%29%28x%2B3%29%28x-3%29%29