To simplify the expression 𝑥+4 / 𝑥−4 - (5𝑥+20 / 𝑥^2 -16), we need to find a common denominator.
The first fraction already has a common denominator of (𝑥−4), so we don't need to do anything with that term.
For the second fraction, we can factor the denominator as (𝑥+4)(𝑥-4). Therefore, the common denominator for both fractions is (𝑥+4)(𝑥−4).
Now, let's rewrite the fractions with the common denominator:
𝑥+4 / 𝑥−4 = (𝑥+4)(𝑥+4) / (𝑥−4)(𝑥+4)
5𝑥+20 / 𝑥^2 -16 = 5(𝑥+4) / (𝑥−4)(𝑥+4)
Now, we can combine the fractions:
(𝑥+4)(𝑥+4) / (𝑥−4)(𝑥+4) - 5(𝑥+4) / (𝑥−4)(𝑥+4)
To subtract the fractions, we need to have a common denominator, which we already have. So, we can combine the numerators:
(𝑥+4)(𝑥+4) - 5(𝑥+4) / (𝑥−4)(𝑥+4)
Next, we can simplify the numerator:
(𝑥+4)(𝑥+4) - 5(𝑥+4) = 𝑥^2 + 8𝑥 + 16 - 5𝑥 - 20
Now, let's combine like terms in the numerator:
𝑥^2 + 8𝑥 + 16 - 5𝑥 - 20 = 𝑥^2 + 3𝑥 - 4
Now, our simplified expression is:
(𝑥^2 + 3𝑥 - 4) / (𝑥−4)(𝑥+4)
Simplify 𝑥+4
𝑥−4
−
5𝑥+20
𝑥
2 −16Simplify 𝑥+4
𝑥−4
−
5𝑥+20
𝑥
2 −16
1 answer