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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?
• 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.
• I'm confused, if we're multiplying both sides by 4k-3, why does the 11 remain?
• 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.
• 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).
• 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 :)