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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

Respuesta :

semsee45

Answer:

[tex]\textsf{b.} \quad g(x) = 1 + \dfrac{10}{x}[/tex]

Step-by-step explanation:

Given rational function:

[tex]g(x)=\dfrac{x+10}{x}[/tex]

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

[tex]\boxed{\dfrac{a+b}{c}=\dfrac{a}{c}+\dfrac{b}{c}}[/tex]

Therefore:

[tex]\implies g(x)=\dfrac{x}{x}+\dfrac{10}{x}[/tex]

[tex]\textsf{Apply the fraction rule}: \quad \dfrac{a}{a}=1[/tex]

[tex]\implies g(x)=1+\dfrac{10}{x}[/tex]

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