Please Simplify:
1 4
--- + ---
x+2 x^2-4
The board won't space as you want it to space. You will need to retype your question using parentheses and / for divide. For example, if you meant,\
[1/(x+2)] + [.... etc)].
Sorry about that! here it is again!
1/x+2 + 4/x^2-4
1 / (x+2) + 4 / [(x+2)(x-2)]
= (x-2) / [(x+2)(x-2) ] + 4 / [(x+2)(x-2)]
= (x+2) / [(x+2)(x-2)]
= 1/(x-2)
To simplify the expression (1/(x+2)) + (4/(x^2-4), we need to find a common denominator.
The first fraction has a denominator of (x+2), and the second fraction has a denominator of (x^2-4).
Now, let's factor the denominator of the second fraction, which is a difference of squares:
x^2 - 4 = (x+2)(x-2)
So, the common denominator is (x+2)(x-2).
To make the first fraction have the common denominator, we multiply the numerator and denominator by (x-2):
(1/(x+2)) * ((x-2)/(x-2)) = (x-2)/((x+2)(x-2))
Now, we have the following expression with a common denominator:
[(x-2)/((x+2)(x-2))] + (4/((x+2)(x-2)))
Combining the fractions, we get:
[(x-2) + 4]/((x+2)(x-2))
Simplifying the numerator, we have:
x - 2 + 4 = x + 2
Therefore, the simplified expression is:
(x + 2)/((x+2)(x-2))
Notice that the (x-2) terms in the numerator and denominator cancel out, leaving us with:
1/(x+2)