SOLUTION: I am really struggling with Rational Expressions with Unlike Denominators. For example, this one I cannot match to the answer: a/4a^2-1 + 4/2a-1 +2. If you could please help me

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: I am really struggling with Rational Expressions with Unlike Denominators. For example, this one I cannot match to the answer: a/4a^2-1 + 4/2a-1 +2. If you could please help me      Log On


   

Question 196726: I am really struggling with Rational Expressions with Unlike Denominators. For example, this one I cannot match to the answer: a/4a^2-1 + 4/2a-1 +2. If you could please help me, I'd appreciate it
Found 2 solutions by jim_thompson5910, stanbon:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
a%2F%284a%5E2-1%29%2B4%2F%282a-1%29%2B2 Start with the given expression.


a%2F%28%282a-1%29%282a%2B1%29%29%2B4%2F%282a-1%29%2B2 Factor the first denominator.


Take note that the LCD is %282a-1%29%282a%2B1%29


a%2F%28%282a-1%29%282a%2B1%29%29%2B%284%282a%2B1%29%29%2F%28%282a-1%29%282a%2B1%29%29%2B2 Multiply the second fraction by %282a%2B1%29%2F%282a%2B1%29 to get the denominator equal to the LCD.


a%2F%28%282a-1%29%282a%2B1%29%29%2B%288a%2B4%29%2F%28%282a-1%29%282a%2B1%29%29%2B2 Distribute


Multiply the third term "2" by %28%282a-1%29%282a%2B1%29%29%2F%28%282a-1%29%282a%2B1%29%29 to get the denominator equal to the LCD.


Multiply


FOIL


Distribute


%28a%2B8a%2B4%2B8a%5E2-2%29%2F%28%282a-1%29%282a%2B1%29%29 Now that all the denominators are equal, we can combine the fractions.


%288a%5E2%2B9a%2B2%29%2F%28%282a-1%29%282a%2B1%29%29 Combine like terms.


%288a%5E2%2B9a%2B2%29%2F%284a%5E2-1%29 FOIL the denominator.


So a%2F%284a%5E2-1%29%2B4%2F%282a-1%29%2B2=%288a%5E2%2B9a%2B2%29%2F%284a%5E2-1%29 where a%3C%3E-1%2F2, or a%3C%3E1%2F2



Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
a/4a^2-1 + 4/2a-1 +2
--------
lcd: 4a^2 -1
-------------
Rewrite each fraction with the lcd as its denominator:
---
a/lcd + 4(2a+1)/lcd + 2(4a^2-1)/lcd
----
Combine the numerators over the lcd:
[a + 4(2a+1) + 2(4a^2-1)]/lcd
---
Simplify the numerator:
[a + 8a + 4 + 8a^2 - 2]/lcd
[8a^2 + 9a + 2]/[4a^2-1]
=============================
Cheers,
Stan H.