Simplify the rational expression. State any excluded values. \frac{7x - 14}{x - 2} A. x B. 7;...

Question:

Simplify the rational expression. State any excluded values.

{eq}\displaystyle \frac{7x - 14}{x - 2} {/eq}

A. {eq}\; x {/eq}

B. {eq}\; 7; \textrm{ where } x \neq -7 {/eq}

C. {eq}\; 7; \textrm{ where } x \neq 2 {/eq}

D. {eq}\; 0 {/eq}

Excluded Value:

An excluded value of an expression is the value of a variable where the expression is not defined. For example, a fraction is not defined when its denominator is zero. So the excluded value of the fraction {eq}\dfrac{1}{x} {/eq} is {eq}x=0 {/eq}.

Answer and Explanation:

The given function is:

$$y = \dfrac{7x - 14}{x - 2} = \dfrac{7(x-2)}{(x-2)}= \boxed{\mathbf{7}} $$

We know that a fraction is not defined when its denominator is zero.

So for excluding values, we set the denominator to zero and solve.

$$x-2=0 \\ \text{Adding 2on both sides}, \\ x= \boxed{\mathbf{2}} $$

Therefore, {eq}y=7, \text{ where } x \neq 2 {/eq}.

Therefore, the answer is option (C).


Learn more about this topic:

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Expressions of Rational Functions

from Precalculus: High School

Chapter 13 / Lesson 4
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