Question

Solve each equation. $$\frac{6}{x}+\frac{40}{x+5}=7$$

Name: Problem 29, Chapter 6: Intermediate Algebra
Uploaded: 2022-03-29T20:17:15-08:00
Duration: 1 min 7 s
Channel: Victor Salazar
Description: Solve each equation. (6)/(x)+(40)/(x+5)=7

   Solve each equation.
$$\frac{6}{x}+\frac{40}{x+5}=7$$

Intermediate Algebra

Jerome E. Kaufmann,… 10th Edition

Chapter 6, Problem 29

Instant Answer

Solved by Expert Victor Salazar

03/29/2022

Step 1

We can do this by multiplying every term by $x(x+5)$, which is the least common multiple of $x$ and $x+5$. This gives us: $$6(x+5) + 40x = 7x(x+5)$$ Show more…

Show all steps

Thanks for your feedback!

Solve each equation. $$\frac{6}{x}+\frac{40}{x+5}=7$$

Play audio

Feedback

Victor Salazar and 61 other subject Algebra 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 involve fractions that contain variables in the denominators. Solving these equations requires special attention to the structure of the fractions and the conditions under which they are defined.

Domain Restrictions

Domain restrictions are critical in rational equations because the denominators cannot be zero. Identifying such restrictions at the outset prevents considering invalid or extraneous solutions.

Clearing Fractions

Clearing fractions by multiplying both sides of the equation by the least common denominator (LCD) is a key technique. This process eliminates the fractions and converts the equation into a polynomial form that is generally easier to solve.

Quadratic Equations

After common denominators are cleared, the resulting equation may be quadratic in form. Solving quadratic equations using methods like factoring, the quadratic formula, or completing the square is a fundamental skill in algebra.

Please give Ace some feedback