SOLUTION: Hi, I'm confused as to how to get to the answer (I already have the answer but I don't understand the solution) of this equation: 4/(a^2-a-2) + 3/(a^2-4) = (7a+11)/(a-2)(a+2)(a+1)

Algebra ->  Numeric Fractions Calculators, Lesson and Practice -> SOLUTION: Hi, I'm confused as to how to get to the answer (I already have the answer but I don't understand the solution) of this equation: 4/(a^2-a-2) + 3/(a^2-4) = (7a+11)/(a-2)(a+2)(a+1)      Log On


   

Question 1017815: Hi, I'm confused as to how to get to the answer (I already have the answer but I don't understand the solution) of this equation:
4/(a^2-a-2) + 3/(a^2-4) = (7a+11)/(a-2)(a+2)(a+1)
How did the ending answer have three bracket multiplications in the denominator?
Could you please explain this answer in clear steps? Thank you very, very much! :D
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
4%2F%28a%5E2-a-2%29+%22%22%2B%22%22+3%2F%28a%5E2-4%29

Factor the denominators:

4%2F%28%28a%2B1%29%28a-2%29%29+%22%22%2B%22%22+3%2F%28%28a-2%29%28a%2B2%29%29

The LCD is %28a%2B1%29%28a-2%29%28a%2B2%29

The denominator in the first term needs the
factor (a+2) in order to equal the LCD, so
we multiply the first term by red%28%28%28a%2B2%29%29%2F%28%28a%2B2%29%29%29
which equals 1 and therefore will not change
the value when we multiply the first term by it.

The denominator in the second term needs the
factor (a+1) in order to equal the LCD, so
we multiply the second term by red%28%28%28a%2B1%29%29%2F%28%28a%2B1%29%29%29
which equals 1 and therefore will not change
the value when we multiply the second term by it.

%22%22%2B%22%22

Rewrite each multiplication of fractions as single fractions:

%284red%28%28a%2B2%29%29%29%2F%28%28a%2B1%29%28a-2%29red%28%28a%2B2%29%29%29+%22%22%2B%22%22+%283red%28%28a%2B1%29%29%29%2F%28%28a-2%29%28a%2B2%29red%28%28a%2B1%29%29%29

Distribute to remove the parentheses in the numerators, but
do not multiply the denominators out.

%284a%2B8%29%2F%28%28a%2B1%29%28a-2%29%28a%2B2%29%29+%22%22%2B%22%22+%283a%2B3%29%2F%28%28a-2%29%28a%2B2%29%28a%2B1%29%29

Notice that the denominators of both terms are the same except
for the order of factors, so we will add the terms of the numerator
and have just one fraction term.  We will choose the second
denominator, since that's the order of factors that you have in
your answer:

%284a%2B8%2B3a%2B3%29%2F%28%28a-2%29%28a%2B2%29%28a%2B1%29%29

Combine like terms in the numerator:

%287a%2B11%29%2F%28%28a-2%29%28a%2B2%29%28a%2B1%29%29

Edwin