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

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

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) (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) (Show Source): You can put this solution on YOUR website!
Start with the given expression.

Factor to get

Factor to get

Now looking at the denominators, we have the factors:

, , and

Now simply find the LCM of , , and

So find the unique factors (and the most frequent unique factors) and multiply them to get:

So the LCD is . 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.

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

Multiply.

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

Multiply

Combine the fractions (this is now possible since EVERY fraction has an equal denominator).

Factor the numerator

Highlight the common terms.

Cancel out the common terms.

Simplify

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Answer:

So where or
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