on question 2 if you cancel out the whole denominator won't that just make it 0 and make the the answer /no solution ?

No. If you cancel out the denominator then it would become 1. Thus, the final answer doesn't have a denominator since it is implied that it's denominator is 1.

I have absolutely no idea how you figure out which numbers x cannot equal. I know it says it is the numbers that make the original expression undefined but how do you find that out?

Rational expressions are fractions. Fractions become undefined if the denominator is = 0. For example: 5/0 = undefined. Now, if this was 5/x, then it is undefined only when x=0. So x can't = 0. If you have an expression of: 5/(x-2), then you look at what would make x-2 = 0. If x=2, this fraction would be undefined. When you have a rational expression that you are simplifying, any time you reduce the fraction, you need to ensure that the restrictions associated with the original fraction are maintained. For example: `[(x-2)(x-5)] / [(x-2) (x+7)}` would have restrictions of x not equal 2 or -7 because these both cause the denominator to become 0. At this point, we don't have to explicitly state the restrictions because they can be derived from the expression. have to explicitly Once reduced (we cancel out the common factor of (x-2)), then we have `(x-5) / (x+7)`. To ensure we maintain the original restrictions, we must explicitly state that "x not equal 2" because this can no longer be derived from the expression. Hope this helps.

For question number 3, how does the denominator of the first expression factor into (x−4)(x+2)? Also for the same number why di they included x=/-2 if you can tell that from the simplified expression?

The denominator is: x^2 - 2x - 8. Find factors of -8 that add to the middle term (-2). The factors are -4 and 2. That creates the binomial factors of (x-4)(x+2). The instructions said to select *all* that apply. x not = -2 applies, as does x not = 4 and 3

For the example 2: Why we don't have to care about numerators? if x = -2 for x+2 / x+1, will it be undefined? Why we don't have to specify x != -2 ?

A 0 in the denominator (in your example: `(x+2)/0` ) is undefined, but a numerator in the denominator (in your example: `(0/x+1)`) isn't undefined. 0/x is 0.

For Q3, why do we have to specify x does not equal -2 when this is obvious from the simplified form of the expression too? In the videos Sal only gives the values x is undefined for when that value is not clear in the simplified form

Because the instructions say to.... Follow the instructions. It asked you to select ALL that apply.

On problem # 3 why is X cannot equal -2 when x+2 is part of the remaining expression. I've seen it counted wrong both ways in other examples and I am confused as whether to count it or not. Thanks in advance.

Hello! In this problem, we're not looking for the simplified expression, we're just looking for the values that make that first expression undefined. If you wanted to, you could just stop at the "factor" step and solve for all the x values that make you divide by 0. If they did ask for the simplified expression, then the answer would be (x+3)/(x+2), x ≠ 3, 4 because in this scenario the x ≠ -2 is implied. Hope this clears it up.

So im very confused on how to prove whether it's undefined?? What exactly do you do?

Take just the denominator, then set it equal to zero. Solve that for x. That's where it's undefined. For example: Y=(bla bla bla)/(x-3) Is undefined when x-3=0, or in other words when x-3

Main content

Course: Integrated math 3 > Unit 13

Lesson 6: Multiplying & dividing rational expressions

Multiplying rational expressions

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Learn how to find the product of two rational expressions.

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Hannah Woods
Posted 6 years ago. Direct link to Hannah Woods's post “I have absolutely no idea...”
I have absolutely no idea how you figure out which numbers x cannot equal. I know it says it is the numbers that make the original expression undefined but how do you find that out?
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(5 votes)
Answer
- Kim Seidel
  Posted 6 years ago. Direct link to Kim Seidel's post “Rational expressions are ...”
  Rational expressions are fractions. Fractions become undefined if the denominator is = 0.
  For example: 5/0 = undefined.
  Now, if this was 5/x, then it is undefined only when x=0. So x can't = 0.
  If you have an expression of: 5/(x-2), then you look at what would make x-2 = 0. If x=2, this fraction would be undefined.
  
  When you have a rational expression that you are simplifying, any time you reduce the fraction, you need to ensure that the restrictions associated with the original fraction are maintained.
  For example:
  [(x-2)(x-5)] / [(x-2) (x+7)} would have restrictions of x not equal 2 or -7 because these both cause the denominator to become 0. At this point, we don't have to explicitly state the restrictions because they can be derived from the expression. have to explicitly
  Once reduced (we cancel out the common factor of (x-2)), then we have (x-5) / (x+7). To ensure we maintain the original restrictions, we must explicitly state that "x not equal 2" because this can no longer be derived from the expression.
  
  Hope this helps.
  Comment on Kim Seidel's post “Rational expressions are ...”
  (10 votes)
Emma Baumgartel
Posted 8 years ago. Direct link to Emma Baumgartel's post “on question 2 if you canc...”
on question 2 if you cancel out the whole denominator won't that just make it 0 and make the the answer /no solution ?
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(6 votes)
Answer
- Ali Anees
  Posted 8 years ago. Direct link to Ali Anees's post “No. If you cancel out the...”
  No. If you cancel out the denominator then it would become 1. Thus, the final answer doesn't have a denominator since it is implied that it's denominator is 1.
  Comment on Ali Anees's post “No. If you cancel out the...”
  (7 votes)
Ashley Valdez
Posted 5 years ago. Direct link to Ashley Valdez's post “For example 2, the answer...”
For example 2, the answer x +2/x+1 has two Xs. Can't those Xs be cancelled?
Button navigates to signup pageComment on Ashley Valdez's post “For example 2, the answer...”
(6 votes)
Answer
- may lin
  Posted 3 years ago. Direct link to may lin's post “No, because the x is not ...”
  No, because the x is not a factor like say;
  
  x(x+2)/x(x+4) it's a common factor so the x can be canceled out
  
  x+2/x+1, you can't cancel out the x because say x = 1
  
  2+1/1+1 = 3/2
  
  if you were to cancel out the 1 (or x) you'd get 2/1=2 which is not the same as 3/2.
  
  this is because it's not something that you factored out from both numerator and denominator, it's something you're adding/subtracting which could change the value.
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  (1 vote)
Apolonio, Morgan
Posted 7 years ago. Direct link to Apolonio, Morgan's post “For question number 3, ho...”
For question number 3, how does the denominator of the first expression factor into (x−4)(x+2)? Also for the same number why di they included x=/-2 if you can tell that from the simplified expression?
Button navigates to signup pageComment on Apolonio, Morgan's post “For question number 3, ho...”
(3 votes)
Answer
- Kim Seidel
  Posted 7 years ago. Direct link to Kim Seidel's post “The denominator is: x^2 ...”
  The denominator is: x^2 - 2x - 8. Find factors of -8 that add to the middle term (-2). The factors are -4 and 2.
  That creates the binomial factors of (x-4)(x+2).
  
  The instructions said to select all that apply. x not = -2 applies, as does x not = 4 and 3
  Button navigates to signup page
  (4 votes)
N N
Posted 3 years ago. Direct link to N N's post “For the example 2: Why we...”
For the example 2:
Why we don't have to care about numerators? if x = -2 for x+2 / x+1, will it be undefined? Why we don't have to specify x != -2 ?
Button navigates to signup pageComment on N N's post “For the example 2: Why we...”
(3 votes)
Answer
- 𝐢ᴀɴᴅʏ_Qɪ
  Posted 3 years ago. Direct link to 𝐢ᴀɴᴅʏ_Qɪ's post “A 0 in the denominator (i...”
  A 0 in the denominator (in your example: (x+2)/0 ) is undefined, but a numerator in the denominator (in your example: (0/x+1)) isn't undefined. 0/x is 0.
  Button navigates to signup page
  (2 votes)
Chris McKnight
Posted 8 years ago. Direct link to Chris McKnight's post “For Q3, why do we have to...”
For Q3, why do we have to specify x does not equal -2 when this is obvious from the simplified form of the expression too? In the videos Sal only gives the values x is undefined for when that value is not clear in the simplified form
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(1 vote)
Answer
- Kim Seidel
  Posted 8 years ago. Direct link to Kim Seidel's post “Because the instructions ...”
  Because the instructions say to.... Follow the instructions. It asked you to select ALL that apply.
  Comment on Kim Seidel's post “Because the instructions ...”
  (6 votes)
Brandon Kyle Tyson
Posted 7 years ago. Direct link to Brandon Kyle Tyson's post “Find the numerical value ...”
Find the numerical value for
Start Fraction x minus 9 Over 9 End Fraction
x−9/9 when x=13
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(2 votes)
Answer
Kathy Mosca
Posted 4 years ago. Direct link to Kathy Mosca's post “Before simplifying the mu...”
Before simplifying the multiplying of fractions, you can divide out the common factor. true or false
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(2 votes)
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Autumn Rogers
Posted 7 years ago. Direct link to Autumn Rogers's post “So im very confused on ho...”
So im very confused on how to prove whether it's undefined?? What exactly do you do?
Button navigates to signup pageComment on Autumn Rogers's post “So im very confused on ho...”
(0 votes)
Answer
- mahansen42
  Posted 7 years ago. Direct link to mahansen42's post “Take just the denominator...”
  Take just the denominator, then set it equal to zero. Solve that for x. That's where it's undefined. For example:
  
  Y=(bla bla bla)/(x-3)
  
  Is undefined when x-3=0, or in other words when x-3
  Button navigates to signup page
  (4 votes)
Fred Haynes
Posted 3 years ago. Direct link to Fred Haynes's post “On problem # 3 why is X c...”
On problem # 3 why is X cannot equal -2 when x+2 is part of the remaining expression. I've seen it counted wrong both ways in other examples and I am confused as whether to count it or not.

Thanks in advance.
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(1 vote)
Answer
- Andrzej Olsen
  Posted 3 years ago. Direct link to Andrzej Olsen's post “Hello! In this problem, ...”
  Hello!
  
  In this problem, we're not looking for the simplified expression, we're just looking for the values that make that first expression undefined. If you wanted to, you could just stop at the "factor" step and solve for all the x values that make you divide by 0.
  
  If they did ask for the simplified expression, then the answer would be
  (x+3)/(x+2), x ≠ 3, 4
  because in this scenario the x ≠ -2 is implied.
  
  Hope this clears it up.
  Comment on Andrzej Olsen's post “Hello! In this problem, ...”
  (2 votes)

Course: Integrated math 3 > Unit 13

Multiplying rational expressions

What you should be familiar with before taking this lesson

What you will learn in this lesson

Multiplying fractions

Example 1: $\frac{3 x^{2}}{2} \cdot \frac{2}{9 x}$ ‍

Check your understanding

Example 2: $\frac{x^{2} - x - 6}{5 x + 5} \cdot \frac{5}{x - 3}$ ‍

Check your understanding

What's next?

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Integrated math 3

Course: Integrated math 3 > Unit 13

What you should be familiar with before taking this lesson

What you will learn in this lesson

Multiplying fractions

Example 1: 3x22⋅29x‍

Check your understanding

Example 2: x2−x−65x+5⋅5x−3‍

Check your understanding

What's next?

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Example 1: $\frac{3 x^{2}}{2} \cdot \frac{2}{9 x}$ ‍

Example 2: $\frac{x^{2} - x - 6}{5 x + 5} \cdot \frac{5}{x - 3}$ ‍