Main content

## SAT (Fall 2023)

### Course: SAT (Fall 2023) > Unit 10

Lesson 2: Passport to advanced mathematics- Solving quadratic equations — Basic example
- Solving quadratic equations — Harder example
- Interpreting nonlinear expressions — Basic example
- Interpreting nonlinear expressions — Harder example
- Quadratic and exponential word problems — Basic example
- Quadratic and exponential word problems — Harder example
- Manipulating quadratic and exponential expressions — Basic example
- Manipulating quadratic and exponential expressions — Harder example
- Radicals and rational exponents — Basic example
- Radicals and rational exponents — Harder example
- Radical and rational equations — Basic example
- Radical and rational equations — Harder example
- Operations with rational expressions — Basic example
- Operations with rational expressions — Harder example
- Operations with polynomials — Basic example
- Operations with polynomials — Harder example
- Polynomial factors and graphs — Basic example
- Polynomial factors and graphs — Harder example
- Nonlinear equation graphs — Basic example
- Nonlinear equation graphs — Harder example
- Linear and quadratic systems — Basic example
- Linear and quadratic systems — Harder example
- Structure in expressions — Basic example
- Structure in expressions — Harder example
- Isolating quantities — Basic example
- Isolating quantities — Harder example
- Function notation — Basic example
- Function notation — Harder example

© 2023 Khan AcademyTerms of usePrivacy PolicyCookie Notice

# Radical and rational equations — Basic example

Watch Sal work through a basic Radical and rational equations problem.

## Want to join the conversation?

- Why is it called RATIONAL equations instead of just, say, equations?(9 votes)
- It's a description helping to classify what kind of equation it is. The term "rational equation" indicates that there is a denominator in the equation.(6 votes)

- I'm confused, if we're multiplying both sides by 4k-3, why does the 11 remain?(2 votes)
- If you multiply 3/2 by 2, what do you get? 3.

If you multiply 15/31 by 31, what do you get? 15.

If you multiply 11/(4k-3) by (4k-3), what do you get? 11.(11 votes)

- Don't you guys know the criss cross method?(5 votes)
- I'm still waiting for the other methods he talked about😂(4 votes)
- I see your comments in every section, when is your test?(1 vote)

- it took 5sec to solve. 🥷

Thanks khanacademy for the lessons.(2 votes) - why do we leave the answer in improper fraction instead of simplifying?(1 vote)
- Since 17 is a prime number, the fraction can not be simplified. Also, in math, mixed numbers are not the preferred method of displaying fractions because mixed numbers sometimes look similar to improper fractions. 3 and 1/2 (which is 3.5) looks quite similar to 31/2 (which is 15.5).(2 votes)

- do anyone know how to type square root symbol(1 vote)
- On a mac, it's [OPTION + V]. On a windows desktop, it's [ALT+251] on the number pad. On anything, you can probably look up a square root symbol online and just copy and paste, or use the insert special character function on any word processor program you may be using.(2 votes)

- It would be easier imo to flip flop all terms and therefore work with more fractions, which I am more comfortable with but I see how a lot of people would disagree(1 vote)
- Isn't functions include radicals are NOT rational functions?

Here you talk about rational equations. So do you mean rational equations can contain radicals? I'm very confused. :((1 vote) - two equations two unknowns(1 vote)

## Video transcript

- [Instructor] What is the
solution to the equation above? So we just need to solve for k. So one thing that we could do, well, there's a couple of
ways that we could do it. One way is we can multiply both sides of this equation times four k minus three. So let's just do that. Four k minus three. It gets the four k minus
three out of the denominator because four k minus three
divided by four k minus three. As long as we assume four k
minus three isn't equal to zero, that's just going to cancel
out and be equal to one. And so this equation is going to simplify to four k minus three times two. And we can actually distribute this two. So this becomes two
times four k is eight k. And then two times negative
three is negative six. So eight k minus six is equal to, well, all we're left with is 11 over one, or we can just write 11. And so adding six to both sides, you could add six to both sides, and so those add up to zero. You're left with eight k is equal to 17. Now we can just divide
both sides by eight, and we get k is equal to 17 over eight. K is equal to 17 over eight.