Question

In the following exercises, evaluate the rational expression for the given values. $\frac{2 x}{x-1}$ (a) $x=0$ (b) $x=2$ (c) $x=-1$

Name: Problem 5, Chapter 8: Elementary Algebra
Uploaded: 2021-07-14T17:09:47-08:00
Duration: 2 min 18 s
Channel: Chris Wojturski
Description: In the following exercises, evaluate the rational expression for the given values. (2 x)/(x-1) (a) x=0 (b) x=2 (c) x=-1

   In the following exercises, evaluate the rational expression for the given values.
$\frac{2 x}{x-1}$
(a) $x=0$
(b) $x=2$
(c) $x=-1$

Elementary Algebra

Lynn Marecek 1st Edition

Chapter 8, Problem 5

Instant Answer

Solved by Expert Chris Wojturski

07/14/2021

Step 1

- Substitute $x = 0$ into the expression: \[ \frac{2 \times 0}{0 - 1} = \frac{0}{-1} = 0 \] - Therefore, when $x = 0$, the value of the expression is $0$. Show more…

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In the following exercises, evaluate the rational expression for the given values. $\frac{2 x}{x-1}$ (a) $x=0$ (b) $x=2$ (c) $x=-1$

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Key Concepts

Rational Expressions

A rational expression is a fraction where both the numerator and the denominator are polynomials. Evaluating or simplifying these expressions requires careful consideration of the algebraic structure and operations involved, particularly because division by zero issues may arise if the denominator becomes zero.

Substitution

Substitution involves replacing the variable in an algebraic expression with a specific value. When evaluating expressions, this method allows you to compute numerical results by directly inserting the provided numbers into the expression.

Domain Restrictions

When working with rational expressions, it's important to understand domain restrictions. Specifically, the expression is undefined for values that make the denominator equal to zero. This check ensures that you only substitute values that result in a defined, meaningful expression.

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