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Math Help - Simplifying Fractions - Am I right?

  1. #1
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    Simplifying Fractions - Am I right?

    Instruction: Write a single fraction with one numerator and one denominator.

    Problem#1:

    1/x + 1/y
    I think the answer should be x+y/xy, yes?


    Problem #2:

    (5a^-1 + 2b^-1) / (3a^-2 - 2b^-2)
    I think the answer should be (3a-b) / 5, yes?


    Problem #3:
    [9-(1/y^2)] / [9+ (6/y) + (1/y^2)]
    I think the answer should be 1 / (6/y), yes?


    Problem #4 says to factor completely:
    18y^3 + 48y^2 + 42y
    I think the final answer should be 6y(3y^2 + 8y + 7), yes?


    Thank you!
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  2. #2
    dan
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    Quote Originally Posted by tesla1410
    Instruction: Write a single fraction with one numerator and one denominator.

    Problem#1:

    1/x + 1/y
    I think the answer should be 1/x+y, yes?
     a/b + c/d  =[  (ad)+(bc)]/ bd
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  3. #3
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    Quote Originally Posted by tesla1410
    Instruction: Write a single fraction with one numerator and one denominator.
    (5a^-1 + 2b^-1) / (3a^-2 - 2b^-2)
    I think the answer should be (3a-b) / 5, yes?
    \frac{5a^{-1}+2b^{-1}}{3a^{-2}-2b^{-2}} = \frac{\frac{5}{a}+\frac{2}{b}}{\frac{3}{a^2}-\frac{2}{b^2}}

     = \frac{\frac{5}{a}+\frac{2}{b}}{\frac{3}{a^2}-\frac{2}{b^2}} \cdot \frac{a^2b^2}{a^2b^2} = \frac{ \left ( \frac{5}{a}+\frac{2}{b} \right ) a^2b^2}{ \left ( \frac{3}{a^2}-\frac{2}{b^2} \right ) a^2b^2}

    = \frac{5ab^2 + 2a^2b}{3b^2 - 2a^2}

    = \frac{ab(5b + 2a)}{3b^2 - 2a^2}.

    I didn't look at 3, since it's the same method as above, but 1 and 4 look good now.

    -Dan
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  4. #4
    dan
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    Quote Originally Posted by tesla1410
    Problem #4 says to factor completely:
    18y^3 + 48y^2 + 42y
    I think the final answer should be 6y(3y^2 + 8y + 7), yes?
    this looks good
    i dont have time now for the others ...maybe some one else can help
    dan
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    Quote Originally Posted by tesla1410
    Problem #3:
    [9-(1/y^2)] / [9+ (6/y) + (1/y^2)]
    I think the answer should be 1 / (6/y), yes?
    <br />
\frac{9-\frac{1}{y^2}}{9+\frac{6}{y}+\frac{1}{y^2}}
    Multiply demoninator and numerator by y^2,
    \frac{9y^2-1}{9y^2+6y+1}=\frac{(3y-1)(3y+1)}{(3y+1)(3y+1)}
    Thus,
    \frac{3y-1}{3y+1}
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    Simplifying Fraction - Am I Right? Part 2

    You guys are great for helping.

    Let me see if I'm getting the hang of it now.

    Is this right?

    [(x+1)/x] / [(x-3)/4]

    To get rid of the fractions, I'll multiply the denominator and numerator by 4x.

    The result is 4x + 4 / x^2 - 3x, which can be reduced to

    4(x+1)/x(x-3)

    Am I right this time?
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  7. #7
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    Quote Originally Posted by tesla1410
    Am I right this time?
    Yes
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  8. #8
    dan
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    Cool

    Quote Originally Posted by tesla1410
    You guys are great for helping.

    Let me see if I'm getting the hang of it now.

    Is this right?

    [(x+1)/x] / [(x-3)/4]

    To get rid of the fractions, I'll multiply the denominator and numerator by 4x.

    The result is 4x + 4 / x^2 - 3x, which can be reduced to

    4(x+1)/x(x-3)

    Am I right this time?

    nice work...i think you got it
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    Simplify Fractions - Am I Right? Part 3

    I'm on a roll. I am fairly certain I have the first 2 problems correct, but the last 2 are trickier.

    1. [5-(1/a)] / (a+b)

    Final answer is (5a-1) / [a(a+b)]


    2. [(2x +1) / (x^2 - 25)] / [(4x^2 -1) / (x-5)]

    Final answer is (2x + 1) / [(4x^2 -1)(x+5)]


    3. {[1/(x+h)] - (1/x)} / h

    For this one, I multiplied the denominator & numerator by x(x+h) and eventually ended with a final answer of [x-(x+h)] / [xh(x + h)], which I don't think can be further simplified.


    4. (x-y) / [(the square root of x) + (the square root of y)]

    I don't think this can be simplified any further. (?)

    Thank you for helping me - I am learning a lot.
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  10. #10
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    Quote Originally Posted by tesla1410
    4. \frac{x-y}{\sqrt x+\sqrt y}

    I don't think this can be simplified any further. (?)
    There is a rule in math that says "A fraction is not completely simplified until you rationalize the denominator"
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    Quote Originally Posted by tesla1410


    3. {[1/(x+h)] - (1/x)} / h

    For this one, I multiplied the denominator & numerator by x(x+h) and eventually ended with a final answer of [x-(x+h)] / [xh(x + h)], which I don't think can be further simplified.
    The first two did not dim my eye. Perhaps they are correct.
    This one did.
    It can be simplified.
    [x-(x+h)]=h

    (x-y) / [(the square root of x) + (the square root of y)]
    It can.

    x-y=(\sqrt{x})^2-(\sqrt{y})^2
    Difference of two squares.
    \frac{(\sqrt{x}-\sqrt{y})(\sqrt{x}+\sqrt{y})}{\sqrt{x}+\sqrt{y}}= \sqrt{x}-\sqrt{y}
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    Simplifying Fractions - Part 3

    Quote Originally Posted by Quick
    There is a rule in math that says "A fraction is not completely simplified until you rationalize the denominator"

    OK... so let me give this a try.

    The original problem is: (x-y) / (square root of x) + (square root of y)

    If I rationalize the denominator, I'd be multiplying it and the numerator by the (square root of x) + (square root of y)......right?

    So, I end up with:

    (x-y)[(square root of x) + (square root of y)] / (x+y)

    And this can't be simplified further.

    Am I right??
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  13. #13
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    Quote Originally Posted by tesla1410
    OK... so let me give this a try.

    The original problem is: (x-y) / (square root of x) + (square root of y)

    If I rationalize the denominator, I'd be multiplying it and the numerator by the (square root of x) + (square root of y)......right?

    So, I end up with:

    (x-y)[(square root of x) + (square root of y)] / (x+y)

    And this can't be simplified further.

    Am I right??
    Hacker solved this, but I would like to pount out that your calculations are wrong anyway...
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  14. #14
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    Quote Originally Posted by tesla1410
    OK... so let me give this a try.

    The original problem is: (x-y) / (square root of x) + (square root of y)

    If I rationalize the denominator, I'd be multiplying it and the numerator by the (square root of x) + (square root of y)......right?

    So, I end up with:

    (x-y)[(square root of x) + (square root of y)] / (x+y)

    And this can't be simplified further.

    Am I right??
    If you choose to ignore my method and use rationalization instead:
    \frac{x-y}{\sqrt{x}+\sqrt{y}}\cdot \frac{\sqrt{x}-\sqrt{y}}{\sqrt{x}-\sqrt{y}}
    The denominator is,
    (\sqrt{x}+\sqrt{y})\cdot (\sqrt{x}-\sqrt{y})=x-y
    Thus,
    \frac{(x-y)(\sqrt{x}+\sqrt{y})}{x-y}
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