add, express answer in simplest form
4x/x^2-18x+72 + 4/x-6
For this question to make sense, I will assume you meant:
4x/(x^2-18x+72) + 4/(x-6)
the first denominator factors to (x-6)(x-12), so it becomes your lowest common denominator
then
4x/(x^2-18x+72) + 4/(x-6)
= 4x/[(x-6)(x-12)] + 4/(x-6)
=[4x(x-6) + 4] / [(x-6)(x-12)]
= [4x^2 - 24x + 4} / [(x-6)(x-12)]
(really not much of a "simplification" problem), the original looks even simpler.
subtract 4x/x-8-32/x-8
-2x > x-12
To add these fractions and express the answer in the simplest form, we need to find a common denominator. The denominators in this case are (x^2 - 18x + 72) and (x - 6).
First, let's factor the polynomial in the first denominator, x^2 - 18x + 72:
x^2 - 18x + 72 = (x - 6)(x - 12)
Now, we have a common denominator of (x - 6)(x - 12). We can rewrite the fractions with this common denominator:
4x/(x^2 - 18x + 72) + 4/(x - 6) = 4x/((x - 6)(x - 12)) + 4/(x - 6)
Since the denominators are the same, we can add the numerators:
= (4x + 4)/(x - 6)(x - 12)
Now, we need to simplify the numerator, 4x + 4, if possible.
We can factor out a 4 from the numerator:
= 4(x + 1)/(x - 6)(x - 12)
So, the simplified expression is 4(x + 1)/(x - 6)(x - 12).