Question

The rational function g(x) = x+10/x can be rewritten in the form g(x) = c+ r/x, where c and

r are constants. Which expression is the result?
a. g(x) = x +10/x
b. g(x) = 1 + 10/x
C. g(x)=x- 10/x+10
d. g(x) = 1- 1/x+10

Answer 1

`\textsf{b.} \quad g(x) = 1 + (10)/(x)`

Explanation:

Given rational function:

`g(x)=(x+10)/(x)`

To rewrite the given rational function in the form g(x) = c + r/x where c and r are constants, apply the fraction rule:

`\boxed{(a+b)/(c)=(a)/(c)+(b)/(c)}`

Therefore:

`\implies g(x)=(x)/(x)+(10)/(x)`

`\textsf{Apply the fraction rule}: \quad (a)/(a)=1`

`\implies g(x)=1+(10)/(x)`