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# Simplifying rational expressions: common monomial factors

Sal simplifies the rational expressions (14x²+7x)/(14x) and (17z³+17z²)/(34z³-51z²) by taking common factors and canceling them.

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• at , why doesn't z not equal -1 • This video and all explanations for simplifying rational expressions are in Algebra II. Why appears the skill for it in Algebra basics first? • Algebra Basics is a subset of the easier algebra skills, while Algebra 2 is the full set of skills that are required for Algebra 2. So, if you drew a Venn diagram, Algebra Basics and Algebra 2 would overlap a little. If you learned the Algebra Basics playlist first, then you will see some of those skills in every math course after that. If you did a good job of learning the skills in Algebra Basics then it will be super easy to master those skills when you run into them in the higher courses.
• I don't understand how you find the values that would make the expression undefined. Can somebody please explain? • It's not as hard as it might appear.
Rational expressions are fractions. Fractions become undefined if the denominator = 0 because we can't divide by 0. The rational expressions have variables in the denominator. Thus, depending upon the value of the variable(s) in the denominator, the denominator might or might not = 0. You need to examine the denominator (before simplifying) to find the value(s) of the variable that can cause the denominator to become = 0.
Look at a couple examples:

2x/5: This fraction has no variable in the denominator and the denominator is not currently 0. So, no value needs to be excluded. This fraction can't become undefined.

2/(5x): A variable is in the denominator. So, we need to consider what values can make 5x become 0. We find this by solving: 5x=0 and we get x=0. So, we need to exclude x=0.

Now look at the 2nd example in the video.
[17z^2(z+1)] / [17z^2(2z-3)]
Notice, I'm using the factored version of the fraction before its reduced. Again, we need to look at only the denominator. There are 3 factors in the denominator that contain the variable: 17z, z and (2z-3). If any one of the factors becomes 0, the fraction is undefined. So we look at each factor.
Solve 17z = 0. It becomes 0 when z=0
Solve z = 0. This is already solved and creates the same result as the 1st factor.
Solve 2x-3 = 0. It creates z=3/2.

Put the results together... the values that will make the denominator = 0 are: z=0 and z=3/2. So, we exclude these values.

Hope this helps.
• Y squared + 4
_________ Im super lost on this one. Can you even simplify this?

Y + 2 • I have a quick question to clarify what is meant by "undefined":

I've just done a mastery test (related to this video), where I was asked to simplify (14x^2 + 7x)/(14x), so I took out 7x as a factor and was left with (2x+1)/(2) which can be rewritten as x+1/2. I then had to say what value of x makes the expression undefined. So, I set the denominator of the original expression to zero: 14x = 0, so it's undefined for x = 0. Is this still true for the simplified expression (x+1/2)? Or is the expression only undefined at x=0 for the original expression?

It doesn't really make sense to me that the original expression and the simplified expression can both be undefined for x=0, so is an expression "undefined" only if they're written in a certain way?

Could I take any expression and rewrite it to have x on the denominator in such a way that it would cause it to be undefined? Hopefully this question makes sense!? Thanks! • I'm a little confused. At when Sal says that 0 is undefined, what does that mean exactly? Is 0 an undefined answer? Also is there a reason to write that x does not equal zero for every problem? • What we are avoiding is division by zero.
Since in the example the denominator is 14x, if x=0 then (14)(0)=0 and you have division by zero - not allowed!
Now let's say the denominator was 14 - x. In this case, then, if x was equal to 14 you would have 14-14=0. In this case you would need to say that x does not equal 14 in order to avoid division by zero.
• Also in my school lessons, My "Instructor", Never mentions factoring a numerator number out of the denominator, This may be why I'm so confused, And when your doing factoring, why must you multiply by one if you already know that you are factoring out 17, is it because it is another 17. I think I just answered my own question, but clarification would be amazing! Thank you! • I'm not following. Where are you getting the Zs and 1s from?   