SOLUTION: Hi I'm not sure how to solve this problem and I have looked in my book and can't find similar problems. 1 1 5 ____ - ___ = ___ 4x-12 x^2-9 x-3

Algebra ->  Rational-functions -> SOLUTION: Hi I'm not sure how to solve this problem and I have looked in my book and can't find similar problems. 1 1 5 ____ - ___ = ___ 4x-12 x^2-9 x-3       Log On


   

Question 349516: Hi I'm not sure how to solve this problem and I have looked in my book and can't find similar problems.
1 1 5
____ - ___ = ___
4x-12 x^2-9 x-3

Note: (X^2) is x squared minus 9. I tried to make these look like fractions but it should read; 1 over 4x minus 12 minus 1 over x squared minus nine equals 5 over x minus three.
Thank You!!!!
Found 2 solutions by mananth, jim_thompson5910:
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
1 1 5
____ - ___ = ___
4x-12 x^2-9 x-3
...
1 1 5
____ - ___ - ___ = 0
4x-12 x^2-9 x-3
...
+%281%2F4%28x-3%29%29-+%281%2F%28x%2B3%29%28x-3%29%29-+%285%2F%28x-3%29%29=0
LCD = +4%28x-3%29%28x%2B3%29
%28%28x%2B3%29-4-5%28x%2B3%29%29%2F%284%28x-3%29%28x%2B3%29%29
%28x%2B3-4-5x-15%29%2F%284%28x-3%29%28x%2B3%29%29
%28-4x-16%29%2F%284%28x-3%29%28x%2B3%29%29
-4%28x%2B4%29%2F4%28x-3%29%28x%2B3%29
-%28x%2B4%29%2F%28x-3%29%28x%2B3%29

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
1%2F%284x-12%29-1%2F%28x%5E2-9%29=5%2F%28x-3%29 Start with the given equation.


1%2F%284%28x-3%29%29-1%2F%28x%5E2-9%29=5%2F%28x-3%29 Factor the first denominator.


1%2F%284%28x-3%29%29-1%2F%28%28x%2B3%29%28x-3%29%29=5%2F%28x-3%29 Factor the second denominator.


Take note that the LCD is 4%28x%2B3%29%28x-3%29


Multiply EVERY term by the LCD 4%28x%2B3%29%28x-3%29 to clear out the fractions.


x%2B3-4=4%28x%2B3%295 Simplify


x%2B3-4=5%2A4%28x%2B3%29 Rearrange the terms


x%2B3-4=20%28x%2B3%29 Multiply


x%2B3-4=20x%2B60 Distribute.


x-1=20x%2B60 Combine like terms on the left side.


x=20x%2B60%2B1 Add 1 to both sides.


x-20x=60%2B1 Subtract 20x from both sides.


-19x=60%2B1 Combine like terms on the left side.


-19x=61 Combine like terms on the right side.


x=%2861%29%2F%28-19%29 Divide both sides by -19 to isolate x.


x=-61%2F19 Reduce.


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Answer:

So the solution is x=-61%2F19



If you need more help, email me at jim_thompson5910@hotmail.com

Also, feel free to check out my tutoring website

Jim