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Math Help - rational expressions

  1. #1
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    rational expressions

    if someone could help me with these seven HW problems. i had do do 75 of them, i just cant figure out these 7! help is much needed..thanks you so much!

    Simplify
    #1. 6t^2-7t-5 all over 2t+1

    #2 q^2-11q+30 Divided by q^2-2q-24
    ------------- -----------
    2q^2-7q-15 q^2-q-20

    #3 4x+12 over 3-x minus 3x+15 over 3-x

    #4 x+3 over x^2-3x-10 minus 2 over x-5

    #5 x^-2-y^-2 over y^-1-x^-1

    Solve the Equation

    #6 3x over x^2-9 Plus 1 over x-3 = 3 over x+3

    Word Problem

    #7 Following a severe snowstorm, Ken and Bettina must clear their driveway and sidewalk. Ken can clear the snow by himself in 4 hours, and bettina can clear the snow be herself in 6 hours. After bettina has been working for 3 hours, ken is able to join her. how much longer will it take them working together to remove the rest of the snow.



    Any help would be much appreciated. Thank You!
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  2. #2
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    Quote Originally Posted by mathnoobie25 View Post
    ...

    Simplify
    #1. 6t^2-7t-5 all over 2t+1

    ...
    Hello,

    \frac{6t^2-7t-5}{2t+1}=\frac{(2t+1)(3t-5)}{2t+1}=3t-5\ , \ t \neq -\frac{1}{2}

    EB
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  3. #3
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    Quote Originally Posted by mathnoobie25 View Post
    ...
    Simplify

    #2 q^2-11q+30 Divided by q^2-2q-24
    ------------- -----------
    2q^2-7q-15 q^2-q-20

    ...
    Hello,

    \frac{q^2-11q+30}{2q^2-7q-15} \div \frac{q^2-2q-24}{q^2-q-20}=


    \frac{(q-6)(q-5)}{(q-5)(2q+3)} \div \frac{(q-6)(q+4)}{(q-5)(q+4)}=. Now transform into a product:

    \frac{(q-6)(q-5)}{(q-5)(2q+3)} \cdot\frac{(q-5)(q+4)}{(q-6)(q+4)}= \frac{q-5}{2q+3}

    EB
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  4. #4
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    Quote Originally Posted by mathnoobie25 View Post
    ...
    Simplify

    #3 4x+12 over 3-x minus 3x+15 over 3-x

    ...
    Hello,

    \frac{4x+12}{3-x} - \frac{3x+15}{3-x}=\frac{x-3}{3-x}=-1

    EB
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  5. #5
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    Quote Originally Posted by mathnoobie25 View Post
    ...

    Simplify

    #4 x+3 over x^2-3x-10 minus 2 over x-5
    ...
    Hello,

    \frac{x+3}{x^2-3x-10} - \frac{2}{x-5}=\frac{x+3}{(x-5)(x+2)} - \frac{2}{x-5}= \frac{x+3}{(x-5)(x+2)} - \frac{2(x+2)}{(x-5)(x+2)}

    =\frac{-x-1}{(x-5)(x+2)}

    EB
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  6. #6
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    Quote Originally Posted by mathnoobie25 View Post
    ...
    Simplify

    #5 x^-2-y^-2 over y^-1-x^-1

    ...
    Hello,

    \frac{x^{-2} - y^{-2}}{y^{-1} - x^{-1}}=\frac{(x^{-1}-y^{-1})(x^{-1}+y^{-1})}{y^{-1} - x^{-1}}= =-(x^{-1}+y^{-1})

    EB
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  7. #7
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    Quote Originally Posted by mathnoobie25 View Post
    ...

    Solve the Equation

    #6 3x over x^2-9 Plus 1 over x-3 = 3 over x+3

    ...
    Hello,

    I assume that you know: x^2-9=(x+3)(x-3)

    \frac{3x}{x^2-9}+\frac{1}{x-3}=\frac{3}{x+3}. Multiply by (x^2-9) (it's the common denominator) and cancel the equal factors out(?):

    3x+x+3=3(x-3). Solve for x. I've got x = -12.

    EB

    PS: to #7. It's raining here, no snow in sight - and by the way it is very late and I'm afraid that I'll make some silly mistakes. So I leave #7 for someone else.
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  8. #8
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    Quote Originally Posted by mathnoobie25 View Post
    ...
    Word Problem

    #7 Following a severe snowstorm, Ken and Bettina must clear their driveway and sidewalk. Ken can clear the snow by himself in 4 hours, and bettina can clear the snow be herself in 6 hours. After bettina has been working for 3 hours, ken is able to join her. how much longer will it take them working together to remove the rest of the snow. ...
    Hello and good morning,

    let S be the total amount of snow which has to be removed

    then
    Ken removes \frac{S}{4} in 1 hour
    Bettina removes \frac{S}{6} in 1 hour

    The complete work could be described by:

    \underbrace{\frac{S}{6} \cdot 3}_{\text{ Bettina working alone}} + \underbrace{\left(\frac{S}{4}+\frac{S}{6}  \right) \cdot x}_{\text{B.+K. working together}} =S. Divide by S:

    \frac{1}{2}+\frac{5}{12}x=1. Solve for x. I've got x = 1.2 hours = 1 hour 12 minutes.

    EB
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