Question

Solve the equations. $$ \frac{w}{5}-\frac{w+3}{w}=-\frac{3}{w} $$

   Solve the equations.
$$
\frac{w}{5}-\frac{w+3}{w}=-\frac{3}{w}
$$

Prealgebra & Introductory Algebra

Prealgebra & Introductory Algebra

Julie Miller, Molly… 2nd Edition

Chapter 14, Problem 27

Instant Answer

Solved by Expert Victor Salazar

04/07/2022

Step 1

This gives us: $$ w^2 - 5w + 15 = -3 $$ Show more…

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Solve the equations. $$ \frac{w}{5}-\frac{w+3}{w}=-\frac{3}{w} $$

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Key Concepts

Algebraic Manipulation

Algebraic manipulation involves operations such as distribution, combining like terms, and isolating the variable to simplify and solve equations. After eliminating the fractions using the LCD, applying these algebraic skills is key to arriving at the correct solution.

Domain Restrictions

When solving rational equations, it is crucial to recognize that any value of the variable that makes a denominator zero must be excluded from the set of possible solutions. Identifying these restrictions early helps prevent the inclusion of extraneous or invalid solutions.

Least Common Denominator (LCD)

The least common denominator is the smallest expression that is a common multiple of all denominators in a rational equation. Multiplying through by the LCD allows one to eliminate fractions, thereby transforming the equation into a simpler form that can be solved using standard algebraic techniques.

Rational Equations

Rational equations are equations that involve fractions with polynomials in the numerator and denominator. They require careful manipulation because the presence of the variable in the denominator can lead to restrictions in the domain and potential extraneous solutions.

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