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Tyro
Asked: 2021-04-13T09:24:43+00:00 In: ,

Solve the equation

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4a/12 + 6a/18 = 12a/24 – 16a/32

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2 Answers

  2. acedstud

    Given \dfrac{4a}{12}+\dfrac{6a}{18}=\dfrac{12a}{24}-\dfrac{16a}{32}, we multiply through by the LCD. That is, the LCM of (12, 18, 24, and 32).

    Expressing the denominators as a product of prime numbers, we have

    12=2\times2\times3=2^2\times3
    18=2\times3\times3=2\times3^2
    24=2\times2\times2\times3=2^3\times3
    32=2\times2\times2\times2\times2=2^5

    Taking the highest powers of the primes, we have that the LCM is 2^5\times3^2=32\times9=288.

    Thus, multiplying through by 288, we have 288\times\dfrac{4a}{12}+288\times\dfrac{6a}{18}=288\times\dfrac{12a}{24}-288\times\dfrac{16a}{32}

    \Rightarrow96a+96a=144a-144a\Rightarrow192a=0\Rightarrow a=0.

  4. Sengemegz
    Best Answer
    Moderator

    \dfrac{4a}{12}+\dfrac{6a}{18}=\dfrac{12a}{24}-\dfrac{16a}{32}

    Divide by the common terms

    \dfrac{a}{3}+\dfrac{a}{3}=\dfrac{a}{2}-\dfrac{a}{2}

    \dfrac{2a}{3}=0

    Cross multiply

    2a=0

    \therefore a=0

     

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