SOLUTION: I need to simplify the following polynomial. I am having trouble finding the LCD. Thanks. y/4y+8 - 1/y^2+2y

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: I need to simplify the following polynomial. I am having trouble finding the LCD. Thanks. y/4y+8 - 1/y^2+2y      Log On


   

Question 186835: I need to simplify the following polynomial. I am having trouble finding the LCD. Thanks.
y/4y+8 - 1/y^2+2y
Found 2 solutions by feliz1965, jim_thompson5910:
Answer by feliz1965(151) About Me  (Show Source):
You can put this solution on YOUR website!
If you do not use parentheses and/or brackets, then the whole thing does not make sense when typed.
Did you mean: y/(4y+8) - 1/(y^2+2y)?
If so, the LCD is the (4y +8)(y^2 + 2y).
Can you take it from here?



Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
y%2F%284y%2B8%29+-+1%2F%28y%5E2%2B2y%29 Start with the given expression.


y%2F%284%28y%2B2%29%29+-+1%2F%28y%5E2%2B2y%29 Factor 4y%2B8 to get 4%28y%2B2%29


y%2F%284%28y%2B2%29%29+-+1%2F%28y%28y%2B2%29%29 Factor y%5E2%2B2y to get y%28y%2B2%29


Now looking at the denominators, we have the factors:

4, y%2B2, y and y%2B2


Now simply find the LCM of 4, y%2B2, y and y%2B2

So find the unique factors (and the most frequent unique factors) and multiply them to get: 4y%28y%2B2%29


So the LCD is 4y%28y%2B2%29. If this does not make any sense, then let me know as it is critical to grasp this concept.


Now the goal is to get EVERY denominator equal to the LCD.



%28y%2Ahighlight%28y%29%29%2F%284%2Ahighlight%28y%29%28y%2B2%29%29+-+1%2F%28y%28y%2B2%29%29 Multiply both the numerator and denominator of the first fraction by y (to get this denominator equal to the LCD)



%28y%5E2%29%2F%284y%28y%2B2%29%29+-+1%2F%28y%28y%2B2%29%29 Multiply.


Multiply both the numerator and denominator by of the second fraction 4 (to get this denominator equal to the LCD)


%28y%5E2%29%2F%284y%28y%2B2%29%29+-+%284%29%2F%284y%28y%2B2%29%29 Multiply


%28y%5E2-4%29%2F%284y%28y%2B2%29%29 Combine the fractions (this is now possible since EVERY fraction has an equal denominator).


%28%28y%2B2%29%28y-2%29%29%2F%284y%28y%2B2%29%29 Factor the numerator


%28highlight%28%28y%2B2%29%29%28y-2%29%29%2F%284y%2Ahighlight%28%28y%2B2%29%29%29 Highlight the common terms.


%28cross%28%28y%2B2%29%29%28y-2%29%29%2F%284y%2Across%28%28y%2B2%29%29%29 Cancel out the common terms.


%28y-2%29%2F%284y%29 Simplify



============================================================

Answer:


So y%2F%284y%2B8%29+-+1%2F%28y%5E2%2B2y%29=%28y-2%29%2F%284y%29 where y%3C%3E-2 or y%3C%3E0