Radical and rational equations — Basic example
About this video
The instructor solves a rational equation for k. Multiplying both sides by 4k minus 3 removes the denominator, provided 4k minus 3 is not zero. He distributes, isolates the variable term, and divides by eight to get k = 17/8.
You'll be able to
- clear a denominator by multiplying both sides by the expression, noting the restriction.
- distribute and combine like terms to isolate the variable.
- check a solution by substituting it back into the original equation.
Key words
- Rational equation
- An equation with a variable in a denominator, which may need to be cleared before solving.
- Restriction
- A value the variable cannot take because it would make a denominator zero.
- Distribute
- Multiply a factor by each term inside a set of parentheses.
- Isolate the variable
- Use inverse operations to get the variable alone on one side of the equation.
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.
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