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## Algebra (all content)

### Course: Algebra (all content)ย >ย Unit 13

Lesson 2: Simplifying rational expressions- Reducing rational expressions to lowest terms
- Reducing rational expressions to lowest terms
- Simplifying rational expressions: common monomial factors
- Reduce rational expressions to lowest terms: Error analysis
- Simplifying rational expressions: common binomial factors
- Simplifying rational expressions: opposite common binomial factors
- Simplifying rational expressions (advanced)
- Reduce rational expressions to lowest terms
- Simplifying rational expressions: grouping
- Simplifying rational expressions: higher degree terms
- Simplifying rational expressions: two variables
- Simplify rational expressions (advanced)
- Simplifying rational expressions (old video)

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# Simplifying rational expressions (old video)

Sal simplifies (28b^6)/(7b) as 4b^5. Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

- How come there are no '' practice this concept'' links @ the top of this page?? just wondering(33 votes)
- What exactly is a monomial?(11 votes)
- A monomial is an expression with one simplified term, like x or 45y. Some other monomials are:

4 (if the monomial contains only one number, without a variable, it is known as a constant)

2xyz

42abcdefghijklmnopqrstuvwxyz

These are not monomials: 5x-9, 3x/5, etc. Monomials can't have negative exponents either.

(An expression with two terms is called a binomial, and one with three terms is a trinomial)(3 votes)

- are there any practices to this?(12 votes)
- Can anyone tell me where to start and end on videos that have to do with Algebra II.

And if there is more than one place to see the Algebra II topics, please list ALL of them.

I'm kind of stuck on topics for the final exam this semester in this class and I can't organize where to watch these videos, so I can fully understand all of Algebra II. I know there is an Algebra I playlist and companion playlists, but I need to know where to get ALL of the Algebra II topics.

Thanks for your help!!!(9 votes) - Can someone explain the b to the fifth power part? I think i got the rest of the video.(4 votes)
- Whenever dividing powers, always subtract the powers. 6-1=5, so the answer is 4b to the fifth power(6 votes)

- what would happen if you had 18x^4/ x? would it be 18x^3?(2 votes)
- Yes, because one x that you factor out of x^4 (x*x^3) and the x in the denominator reduce to 1: 18x^4/x = 18x^3*x/x = 18x^3*1 = 18x^3.(10 votes)

- How do you divide a algebraic expression by a monomial ?

Appreciated greatly if answered(6 votes)- Starting with a binomial divided by a monomial (8x^2-4x) / (2x) ;

Factor the greatest common factor of the numerator 4x*(2x-1) / (2x) ;

Compare the factored numerator to the denominator ;

Notice the greatest common factor (between 4x and 2x) is 2x ;

We divide one factor of the numerator by the denominator 2*(2x-1) / 1 ;

perform some simplifying reductions 4x-2(2 votes)

- what if the two whole numbers are negative(4 votes)
- A negative number times a negative number is a positive number.(1 vote)

- What if b=0? It's in the denominator, so according to our rules (which I don't agree with) we must state b != 0.(3 votes)
- Can this "old" video really teach this concept in 57 seconds? After this video I am more confused than when I had started it...(2 votes)
- I understood it fine but probably because I know the properties of fractions and exponents. It's marked old probably because it's short and he didn't explain why or how he did what he did. You probably should find the new version of this concept to watch.

But in this video, the properties a/b * c/d = ac/bd and a^m / a^n = a^(m-n) were used.(2 votes)

## Video transcript

Simplify the expression 28b
to the sixth divided by 7b. Well this is the same
thing as 28/7 times b to the sixth over b. And I did it this
way so that we have b to the sixth over b
to some other power. And this is over b, which is the
same thing as b to the first. So we could simplify this
using exponent properties. And 28/7 we can just
clearly simplify because 28 is divisible by 7. 28 divided by 7 is just 4. So that is just 4. And then b to the
sixth divided by b to the one, that's just going
to be b to the sixth minus 1 power. So times b to the sixth
minus 1 or b to the fifth. So our answer is
4b to the fifth.