Question

Rewrite the rational function g(x) = x - 4/x in the form g(x) = c + r/x where c and r are constants.

a) g(x) = 1 - 4/x
b) g(x) = -4/x + 1
c) g(x) = -1 - 4/x
d) g(x) = 4/x - 1

Answer 1

To rewrite the rational function g(x) = x - 4/x in the form g(x) = c + r/x, we need to find the values of c and r. The correct answer is g(x) = -1 + (4 - x^2)/x.

Step-by-step explanation:

To rewrite the rational function g(x) = x - 4/x in the form g(x) = c + r/x, we need to find the values of c and r.
To do this, we can use the following steps:

1. Get a common denominator for the expression: x - 4/x
2. Multiply the first term (x) by x and the second term (4/x) by 1 to get a common denominator of x
3. Combine the terms: (x^2 - 4)/x
4. Factor out a -1 from the numerator: (-1)(4 - x^2)/x
5. Now the expression is in the form g(x) = c + r/x, where c = -1 and r = 4 - x^2

Therefore, the correct answer is g(x) = -1 + (4 - x^2)/x.