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## SAT

### Course: SAT > 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

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# 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?(8 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.(5 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.(9 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)

- 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)
- The rules of algebra, especially the addition property of equality, say that if we add 6 to both sides of the equation, we do not change the balance of the equation, and the two sides will remain equal.

So if we have 8k - 6 = 11

we can add 6 to both sides

8k - 6 + 6 = 11 + 6

∴ 8k - 6 + 6 = 11 + 6

8k + 0 = 17

8k = 17 now we use the division property of equality that says that we can divide both sides by the same amount (as long as that amount is not zero)

8/8 k = 17/8

k = 17/8(1 vote) - I have been practicing radical and rational equations and I have a question: When we have for example, root of a-1, we can take the root off by doing a-1^2. But afterwards shouldn't it be absolute value of a-1 because we don't know the exact price of a? Or does Khan Academy take a as a non negative number from the beginning? I hope I didn't confuse you :)(0 votes)

## 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.