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

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

Factor the first denominator.

Take note that the LCD is

Multiply the second fraction by to get the denominator equal to the LCD.

Distribute

Multiply the third term "2" by to get the denominator equal to the LCD.

Multiply

FOIL

Distribute

Now that all the denominators are equal, we can combine the fractions.

Combine like terms.

FOIL the denominator.

So where , or

Answer by stanbon(75887) (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.
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