Multiplying rational expressions (article) | Khan Academy (2024)

Learn how to find the product of two rational expressions.

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  • Hannah Woods

    6 years agoPosted 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?

    (5 votes)

    • Kim Seidel

      6 years agoPosted 6 years ago. Direct link to Kim Seidel's post “Rational expressions are ...”

      Multiplying rational expressions (article) | Khan Academy (4)

      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.

      (10 votes)

  • Emma Baumgartel

    8 years agoPosted 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 ?

    (6 votes)

  • Ashley Valdez

    5 years agoPosted 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?

    (6 votes)

    • may lin

      3 years agoPosted 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.

      (1 vote)

  • Apolonio, Morgan

    7 years agoPosted 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?

    (3 votes)

    • Kim Seidel

      7 years agoPosted 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

      (4 votes)

  • N N

    3 years agoPosted 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 ?

    (3 votes)

    • 𝐢ᴀɴᴅʏ_Qɪ

      3 years agoPosted 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.

      (2 votes)

  • Chris McKnight

    8 years agoPosted 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

    (1 vote)

    • Kim Seidel

      8 years agoPosted 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.

      (6 votes)

  • Brandon Kyle Tyson

    7 years agoPosted 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

    (2 votes)

  • Kathy Mosca

    4 years agoPosted 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

    (2 votes)

  • Autumn Rogers

    7 years agoPosted 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?

    (0 votes)

    • mahansen42

      7 years agoPosted 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

      (4 votes)

  • Fred Haynes

    3 years agoPosted 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.

    (1 vote)

    • Andrzej Olsen

      3 years agoPosted 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.

      (2 votes)

Multiplying rational expressions (article) | Khan Academy (2024)
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