SOLUTION: I need help solving this problem: So far I have this: x/x2+5x+6 - 2/x2+3x+2 x/(x+2)(x+3) - 2/(x+2)(x+1) but I don't know what to do next.

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: I need help solving this problem: So far I have this: x/x2+5x+6 - 2/x2+3x+2 x/(x+2)(x+3) - 2/(x+2)(x+1) but I don't know what to do next.       Log On


   

Question 1151158: I need help solving this problem: So far I have this:
x/x2+5x+6 - 2/x2+3x+2
x/(x+2)(x+3) - 2/(x+2)(x+1) but I don't know what to do next.

Found 2 solutions by MathLover1, jim_thompson5910:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

x%2F%28x%5E2%2B5x%2B6%29+-+2%2F%28x%5E2%2B3x%2B2%29
x%2F%28%28x%2B2%29%28x%2B3%29%29+-+2%2F%28%28x%2B2%29%28x%2B1%29%29 ........common denominator for %28x%2B2%29%28x%2B3%29 and %28x%2B2%29%28x%2B1%29 is %28x%2B2%29%28x%2B3%29%28x%2B1%29

%28x%28x%2B1%29+-+2%28x%2B3%29%29%2F%28%28x%2B3%29%28x%2B2%29%28x%2B1%29%29
%28x%5E2%2Bx+-+2x-6%29%2F%28%28x%2B3%29%28x%2B2%29%28x%2B1%29%29
%28x%5E2+-+x-6%29%2F%28%28x%2B3%29%28x%2B2%29%28x%2B1%29%29
%28%28x+%2B+2%29+%28x+-+3%29%29%2F%28%28x%2B3%29%28x%2B2%29%28x%2B1%29%29....simplify

+%28x+-+3%29%2F%28%28x%2B3%29%28x%2B1%29%29 ...for x%3C%3E2

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Great job so far getting the proper factorizations.

Examine the denominators
(x+2)(x+3) and (x+2)(x+1)

We have the unique factors: (x+2), (x+3) and (x+1)
These unique factors form the Lowest Common Denominator (LCD).
The LCD is (x+1)(x+2)(x+3).

The goal is to get each fraction to have the LCD. For the first fraction we have (x+2)(x+3). What's missing to have this turn into the LCD? That would be (x+1).

So we must multiply top and bottom of the first fraction by (x+1) so we get to the LCD.


The first fraction %28x%29%2F%28%28x%2B2%29%28x%2B3%29%29 turns into %28x%5E2%2Bx%29%2F%28%28x%2B1%29%28x%2B2%29%28x%2B3%29%29 after performing this step.

-------------------------------------------

Now turn to the second fraction
%282%29%2F%28%28x%2B2%29%28x%2B1%29%29
which is the same as
%282%29%2F%28%28x%2B1%29%28x%2B2%29%29


What's missing from the denominator to have it equal to the LCD? That would be (x+3).

Multiply top and bottom of this fraction by (x+3) to get...


So %282%29%2F%28%28x%2B1%29%28x%2B2%29%29 turns into %282x%2B6%29%2F%28%28x%2B1%29%28x%2B2%29%28x%2B3%29%29
-------------------------------------------

To summarize so far:
%28x%29%2F%28%28x%2B2%29%28x%2B3%29%29 turns into %28x%5E2%2Bx%29%2F%28%28x%2B1%29%28x%2B2%29%28x%2B3%29%29

%282%29%2F%28%28x%2B1%29%28x%2B2%29%29 turns into %282x%2B6%29%2F%28%28x%2B1%29%28x%2B2%29%28x%2B3%29%29


From here, we can subtract the fractions as the denominators are both the same.




















Your answer would either be %28x-3%29%2F%28%28x%2B1%29%28x%2B3%29%29 or %28x-3%29%2F%28x%5E2%2B4x%2B3%29 depending on if your teacher wants you keep the denominator factored or not.