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Math Help - common denominator

  1. #1
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    common denominator

    What is the common denominator in this exercise?
    <br />
\frac{a}{3a-5}-\frac{a+1}{3a+5}-\frac{2(5+a)}{25-9a^2}<br />

    <br />
\frac{a}{3a-5}-\frac{a+1}{3a+5}-\frac{2(5+a)}{(5-3a)(5+3a)}<br />

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  2. #2
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    hello
    1) \frac{?}{(25-9a^{2})}
    2) \frac{?}{(5-3a)(5+3a)}
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  3. #3
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    So is (5-3a)(5+3a) the common denominator?
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  4. #4
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    Quote Originally Posted by klik11 View Post
    So is (5-3a)(5+3a) the common denominator?
    yes
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  5. #5
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by klik11 View Post
    So is (5-3a)(5+3a) the common denominator?
    Nope.

    When finding a LCD, forget about the numerators for a second and focus only on the denominators.

    In your problem, what factors would be needed in the last term so that it has it contains the factors of the two other terms?
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  6. #6
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    I was thinking about (5-3a)(5+3a)(-5+3a)...
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  7. #7
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    Quote Originally Posted by VonNemo19 View Post
    Nope.

    When finding a LCD, forget about the numerators for a second and focus only on the denominators.

    In your problem, what factors would be needed in the last term so that it has it contains the factors of the two other terms?
    i think we have  \frac{a}{3a-5}-\frac{a+1}{3a+5}-\frac{2(5+a)}{(5-3a)(5+3a)}=\frac{-a(5+3a)-(a+1)(5-3a)-2(5+a)}{(5-3a)(5+3a) }
    no ?
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  8. #8
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by Raoh View Post
    i think we have  \frac{a}{3a-5}-\frac{a+1}{3a+5}-\frac{2(5+a)}{(5-3a)(5+3a)}=\frac{-a(5+3a)-(a+1)(5-3a)-2(5+a)}{(5-3a)(5+3a) }
    no ?
    Not quite.

    (5-3a)\neq(3a-5) which means we still need (3a-5) as a factor.

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  9. #9
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    Quote Originally Posted by VonNemo19 View Post
    Not quite.

    (5-3a)\neq(3a-5) which means we still need (3a-5) as a factor.

    yes, but (5-3a)=-(3a-5).
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  10. #10
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by Raoh View Post
    yes, but (5-3a)=-(3a-5).
    Well, in that case...

    I apologize.

    Nice work Raoh.
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  11. #11
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    Thanks
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