Question

Answer true or false. $x^{-1}-x^{-2}=\frac{x-1}{x^{2}}$

Name: Problem 10, Chapter 5: Intermediate Algebra
Uploaded: 2022-02-27T05:58:16-08:00
Duration: 13 s
Channel: Erika Bustos
Description: Answer true or false. x^-1-x^-2=(x-1)/(x^2)

   Answer true or false.
$x^{-1}-x^{-2}=\frac{x-1}{x^{2}}$

Intermediate Algebra

Jerome E. Kaufmann,… 10th Edition

Chapter 5, Problem 10

Instant Answer

Solved by Expert Erika Bustos

02/27/2022

Step 1

We can do this by finding a common denominator for the two terms on the left side. The common denominator of $x^{-1}$ and $x^{-2}$ is $x^{2}$. So, we rewrite $x^{-1}$ as $\frac{1}{x}$ and $x^{-2}$ as $\frac{1}{x^{2}}$. Show more…

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Answer true or false. $x^{-1}-x^{-2}=\frac{x-1}{x^{2}}$

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Key Concepts

Negative Exponents

Negative exponents indicate the reciprocal of the base raised to the corresponding positive exponent. For instance, x?¹ is equivalent to 1/x, and x?² is equivalent to 1/x². Recognizing and converting negative exponent notation to its fractional form is essential for simplifying and comparing expressions.

Rational Expression Simplification

Simplifying rational expressions involves combining fractions by finding a common denominator and reducing the expression to its simplest form. In this context, converting terms with negative exponents to fractions and then rewriting the expression to a single fraction is a common technique used to verify the equality of algebraic expressions.

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