What is wrong with the following equation? \frac{x^2 + x - 20}{x - 4} = x + 5 a. (x - 4) (x...

Question:

What is wrong with the following equation?

{eq}\frac{x^2 + x - 20}{x - 4} = x + 5 {/eq}

a. {eq}(x - 4) (x - 5) \neq x^2 + x - 20 {/eq}

b. The left-hand side is not defined for x = 0, but the right-hand side is.

c. The left-hand side is not defined for x = 4, but the right-hand side is.

d. None of these - the equation is correct.

Choose an option and explain.

Domain of Rational Functions:

A function {eq}f(x) {/eq} is called a rational function if it can be written as

{eq}f(x)=\frac{p(x)}{q(x)} {/eq}

where {eq}p(x) {/eq} and {eq}q(x) {/eq} are both polynomials.

The domain of a rational function is all real values for which the denominator is nonzero.

When the denominator is zero at some value {eq}x=a {/eq}, we say that the function is not defined at {eq}x=a {/eq}.

Answer and Explanation:

The correct answer is (c).

The left-hand side of the equation can be factored:

{eq}\frac{x^2+x-20}{x-4}=\frac{(x+5)(x-4)}{x-4} {/eq}

It is...

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Analyzing the Graph of a Rational Function: Asymptotes, Domain, and Range

from Math 105: Precalculus Algebra

Chapter 4 / Lesson 9
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