Question

Solve. $$\frac{\frac{1}{x}+1}{x}=\frac{\frac{1}{x}}{2}$$

   Solve.
$$\frac{\frac{1}{x}+1}{x}=\frac{\frac{1}{x}}{2}$$

Elementary and Intermediate Algebra

Elementary and Intermediate Algebra

Marvin L. Bittinger,… 4th Edition

Chapter 7, Problem 76

Instant Answer

Solved by Expert Anna Jones

05/27/2020

Step 1

This gives us: \[2x \cdot \frac{\frac{1}{x}+1}{x} = 2x \cdot \frac{\frac{1}{x}}{2}\] Show more…

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Solve. $$\frac{\frac{1}{x}+1}{x}=\frac{\frac{1}{x}}{2}$$

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Key Concepts

Domain Restrictions

When variables appear in the denominator, it is crucial to identify values that would make any denominator zero, since division by zero is undefined. These restrictions must be considered to ensure that any solutions obtained are valid for the original equation.

Rational Equations

Rational equations involve expressions that are ratios of polynomials or other algebraic expressions. Solving such equations requires careful manipulation and often involves combining and simplifying fractions, which can lead to linear, quadratic, or higher-order equations.

Complex Fractions

Complex fractions are expressions where fractions appear in the numerator, the denominator, or both. Simplification typically involves rewriting the expression by finding a common denominator or multiplying numerator and denominator by the least common denominator to reduce the expression to a simpler form.

Elimination of Denominators

A common strategy for solving equations with fractions is to multiply both sides of the equation by an appropriate common denominator, which eliminates the fractional components and transforms the equation into a simpler algebraic form. This method must be applied carefully to avoid introducing extraneous solutions.

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