If p(x) = x - 4, q(x) = x^2 + 8, and r(x) = x^2 - 2x - 8, then what is the simplified form of f(x) = x/p(x) - q(x)/r(x)?

To simplify f(x) = x/p(x) - q(x)/r(x), we first need to find the expressions for p(x) and q(x) in terms of x:

p(x) = x - 4
q(x) = x^2 + 8

Now, we need to find the expression for f(x) using the given expressions for p(x) and q(x):

f(x) = x/(x - 4) - (x^2 + 8)/(x^2 - 2x - 8)

Next, we need to find a common denominator for the two fractions in f(x):

f(x) = x(x^2 - 2x - 8)/(x - 4)(x^2 - 2x - 8) - (x^2 + 8)(x - 4)/(x - 4)(x^2 - 2x - 8)

Now, we can combine the fractions:

f(x) = (x^3 - 2x^2 - 8x - x^3 + 4x^2 + 32)/(x - 4)(x^2 - 2x - 8)

f(x) = (2x^2 - 8x + 32)/(x - 4)(x^2 - 2x - 8)

Therefore, the simplified form of f(x) = x/p(x) - q(x)/r(x) is f(x) = (2x^2 - 8x + 32)/(x - 4)(x^2 - 2x - 8).

1/(x - 2)

What is the factory of x^2+8