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### Course: Precalculus>Unit 4

Lesson 6: Multiplying and dividing rational expressions

# Multiplying & dividing rational expressions: monomials

Sal multiplies (6x³/5) X (2/3x) and divides (2x⁴/7) ➗ (5x⁴/4).

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• I didn't really get the difference between the first function being undefined for 0 and the second function being = to 0 when x = 0. Could someone explain the difference between something being undefined and something being = 0?
• When x=0, you will be dividing be 0, which is undefined. Why? Because dividing by 0 is like asking "how many nothings fit into this?" which is a pointless question as it would be infinite nothings that can fit into something.
• I've been trying to solve some problems on Khan Academy related to this subject (I stared before 6 hours) but every time I got the wrong answer! the problem is: I don't understand the notation of undefined! I watched all the videos related to this matter! I can factor, multiply, divide, manipulate..etc, but when it comes to the undefined no way!
Please, can somebody help me understand this?
• If you input a random x, c into a function, f(x), f(x) is undefined at c if the function does not clarify what f(c) is, or if the output is somthing divided by 0 (1/0, 16/0, 0/0, etc.).
I hope that this is helpful!
• I'm confused at , because I thought that (4x^2)/5 was equivalent to 4/5 and (x^2)/5. However, Sal sets it up as 4/5x^2 where x^2 is not being divided by 5. Any reasons why this is so?
• Since you are multiplying x^2 by 4, then proceeding to divide it by 5, doing 4 divided by 5 and then multiplying that my x^2 would yield the same result.
(1 vote)
• Whats a "reciprocal"? ()
• For any fraction, its reciprocal is created by flipping the fraction.
Example:
3/4: its reciprocal is 4/3
-5/2: its reciprocal is -2/5
6: Note 6 as a fraction is 6/1. Its reciprocal = 1/6

In the video, Sal is using the reciprocal of (5x^4)/4, which would be 4/(5x^4).
Hope this helps.
• What do you do when mixing monomials and binomials in the numerator and denominator?
• what is an integer or fraction as m over n in simplest form where m and n are integers?
• m/n is in simplest form is m and n contain no common factors.
• Can't you simplify 8/35?
(1 vote)
• Well, to simplify fractions, you would need to find the greatest comment factor (GCF). 8 and 35 have no common factors other than one, so you would leave the fraction as it is because it is already simplified the most it can.
(1 vote)
• Wow, I didn't know that fractions can be written that way! But which way would a test expect? Wouldn't they both be valid or would one be more simplified than the other?