Let F(x)=(x+3)/(x) and G(x)=(x-4)/(3) Find all x for which F(x)=G(x)

Name: Problem 43, Chapter 11: Elementary and Intermediate Algebra
Uploaded: 2020-07-09T23:51:12-08:00
Duration: 2 min 25 s
Channel: Deboney Harris
Description: Let F(x)=(x+3)/(x) and G(x)=(x-4)/(3) Find all x for which F(x)=G(x)

step 1 All right, so we have this equation f of x and this equation g of x and we'll figure out what x

Let F(x)=(x+3)/(x) and G(x)=(x-4)/(3) Find all x for which...

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

Solving Linear Equations

Once the equation is simplified, it often reduces to a linear equation—a first-degree equation in one variable. Solving linear equations involves isolating the variable on one side of the equation through algebraic manipulation, leading to the solution of the equation.

Cross Multiplication

Cross multiplication is a technique used to solve equations involving fractions or rational expressions. It involves multiplying both sides of the equation by the product of the denominators to eliminate fractions, which simplifies the equation to a form that is easier to solve.

Rational Functions

Rational functions are functions expressed as the quotient of two polynomials. They are significant in algebra because they often have restrictions on their domain and can exhibit behaviors such as asymptotes, holes, or discontinuities when the denominator is zero.

Domain Restrictions

Domain restrictions are conditions that must be met to ensure that the expressions in an equation are defined. In the context of rational functions, any solution that makes a denominator equal to zero must be excluded from the domain, ensuring that the function remains valid.

Transcript

Please give Ace some feedback