Question

Solve. $$\frac{4 x}{x-4}+5=\frac{5 x}{x-4}$$

   Solve.
$$\frac{4 x}{x-4}+5=\frac{5 x}{x-4}$$

Prealgebra and Introductory Algebra

Prealgebra and Introductory Algebra

Richard N. Aufmann,… 3rd Edition

Chapter 11, Problem 30

Instant Answer

Solved by Expert Cory Kuzinski

06/24/2020

Step 1

This gives us: \[4x + 5(x-4) = 5x\] Show more…

Show all steps

lock

Thanks for your feedback!

Solve. $$\frac{4 x}{x-4}+5=\frac{5 x}{x-4}$$

Play audio

Feedback

Powered by NumerAI

Cory Kuzinski and 71 other educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Rational Equations

Rational equations are equations in which one or more terms are rational expressions—fractions whose numerators and denominators are polynomials. Solving these equations involves techniques that ensure proper handling of the expressions while accounting for potential restrictions on the variable.

Domain Restrictions

When dealing with rational equations, it's critical to identify domain restrictions, meaning values of the variable that make any denominator zero. Such values must be excluded from the solution set because division by zero is undefined.

Clearing Denominators

Clearing denominators involves multiplying both sides of the equation by the least common denominator to eliminate the fractional parts. This approach transforms a rational equation into a simpler, typically polynomial, equation that is easier to solve.

Solving Linear Equations

After clearing denominators and simplifying, many rational equations reduce to linear equations. Solving these involves combining like terms and isolating the variable, yielding the solution to the original problem while ensuring all steps are valid within the equation's defined domain.

Recommended Videos

Transcript

Ace is your personal tutor. It breaks down any question with clear steps so you can learn.

Start Using Ace

Continue solving this problem

Create a free account to:

View full step-by-step solution
Ask follow-up questions with Ace AI
Save progress and study later