if x=3: solve (x^2 - 3^2 )/(x - 3) i want to know which answer is correct 0 or 6 ?

Update:

any expert can help because i don't know the answer.

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  • 1 decade ago
    Favorite Answer

    The answer is 6. It can't be 0, because 0/0 is undefined mathematically. The (x-3) factor cancels out, leaving 3+3 = 6.

    (x² - 3²) / (x - 3)

    (x + 3)(x - 3) / (x - 3)

    (x + 3)

    To answer Tom below:

    Technically you're correct that if you apply it directly to the problem at hand, the answer is actually not 6, because this system is undefined, but using calculus and the principles of limits, the answer to this approaches 6 from both sides.

    e.g.

    2.9^2 - 3^2 / 2.9-3 = 5.9

    2.99^2 - 3^2 / 2.99 - 3 = 5.99

    2.999^2 - 3^2 / 2.999 - 3 = 5.999

    3.001^2 - 3^2 / 3.001 - 3 = 6.001

    3.01^2 - 3^2 / 3.01 - 3 = 6.01

    3.1^2 - 3^2 / 3.1 - 3 = 6.1

    etc.

    You can use L'Hopital's rule on the system to actually provide the correct answer, which is 6.

    In that case, you have:

    d/dx(x² - 9 / x - 3)

    2x / 1

    So, if x = 3, the answer is again shown to be 6.

    Source(s): I'm a math major.
  • 1 decade ago

    If you ever took precalculus or some other math class which covers properties of functions, you learn how to determine the domain of the function. One of the red flags to look out for is when you divide by zero. In your expression, when x = 3, the denominator is zero. Thus, the domain is every number beside 3. Unfortunately, the number you are trying to plug in (x = 3) is the only number that doesn't work in this function.

    To see this first hand, you0 can graph this function on a TI-83. If you zoom in on the point of the graph at x = 3, you will see that there is a blank spot there! That is because, as stated above, there just isn't a value of the expression at x = 3.

    You may say, well it looks like the answer should be 6, looking at the graph. This concept of what the answer "should be" is what limits are all about. The values of the function on the left and right of x = 3 all go towards 6 as you get closer and closer. So we say the limit as x goes to 3 is 6.

    So even though it is not technically the answer, 6 is your best choice. Zero is absolutely not correct in any sense. The very best answer is to say that the expression is undefined at x = 3.

    This problem illustrates why 0/0 is called indeterminate. In this problem, 0/0 in a way equals 6. The idea that 0/0 can equal anything is actually the essence of calculus.

    Source(s): I got an A+ in mathematical analysis in college.
  • 1 decade ago

    First of all you have to factor out to say that something cancels out. And since this is clearly a solving the equaiton problem cancelling does not do the trick. Now you have to use the substitution property. And substitute 3 for x So you are left with (3^2-3^2)/(3-3).

    Next you have to use the order of operations ( perentises, exponent, Multi/Divide, Add/ Subtra.) And first you need to do the top portion of the fraction. You will get (9-9) and you can substitute that with "zero"

    Now you have to look at a few rules. the rules state that you can divide in to "zero" but it can not divide in to something. If you divide into "zero" then you will get a slope of "zero" which is a flat horizontal line. But if you get a "zero" on the botom of any

    expression or equation then you get a null set. which is "zero" with a line through it. When graphing that become a vertical line.

    Now lets take a look at the bottom we have (3-3) and we know that this is "zero" and following our rules we must say that there is no solution. so neither is correct. and you may write that on your paper and you will get full credit. for it. Make sure you write an explaination for it. My Pre-cal teacher at USA made us do that so when can show her we know what we are doing.

    I seem to have forgotten that you can seperate the square from the expression Doug is right. maybe we should be friends. And you will never get ifinity when you have a situation like this because infinity means that you will include the answer when you are graphing it. And there is a hole in the graph when X=3 and holes are never apart of the answer so you can say that x is inclusive in the set when (negative infinity, 3) and the union of (3, positive infinity).

  • Anonymous
    1 decade ago

    The first person to answer this question is correct. The answer is undefined. You can't divide nothing by nothing. Just follow pemdas and you will come out to 0/0 which is undefined. 3^2=9

    then 3^2=9 so you have 9-9 for the first parenthesis, and that equals 0. Then all of that is divided by (3-3) which equals 0. So, 0/0 = undefined. There is your answer. Follow pemdas and you won't go wrong.

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  • 1 decade ago

    6

  • 1 decade ago

    Neither of the answers is correct. The answer is undefined

    working; if x=3: (x^2-3^2)/(x-3) = (3^2-3^2)/(3-3)

    = (9-9)/(3-3)

    = 0/0 (undefined)

  • Anonymous
    1 decade ago

    6

  • 1 decade ago

    The answer is 0 (Zero) because the using substitution, the resulting equation is (3^2-3^2)/(3-3) which is (9-9)/(3-3) which really equals 0/0 which is 0.

  • 1 decade ago

    6

  • 1 decade ago

    It's 0

  • Justin
    Lv 5
    1 decade ago

    Doug is correct. The answer is 6... specifically BECAUSE you can't divide by zero. This is why Doug canceled out the denominator making it effectively 1.

    x=3

    (x^2-3^2)/(x-3)

    -working backward to show you-

    (x+3)(x-3)

    x^2+3x-3x-9

    x^2-9

    x^2-3^2

    x^2-3^2=(x+3)(x-3)

    -so subtitute

    (x+3)(x-3)/(x-3)

    -cancel out the (x-3)

    (x+3)*1/1

    (x+3)

    -since x=3

    3+3

    6

    zero cannot be an answer as it is null - you can't divide by zero, this is why you cancel it out - to avoid having to do so.

    I cannot believe how many people don't bother simplifying the equation before solving for the answer. the answer is only in question because no simplification has been done. the lack of simplification is also what is leading to the null answer or 0/0.

    simplify first, THEN solve the problem.

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