solve ,show work and explain?

2/a^2-1=6/a^2-2a-3

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  • Anonymous
    1 decade ago
    Favorite Answer

    Possible intermediate steps:

    2/(a^2-1) = 6/(a^2-2 a-3)

    Cross multiply:

    2 (a^2-2 a-3) = 6 (a^2-1)

    Expand out terms on both sides:

    2 a^2-4 a-6 = 6 a^2-6

    Subtract 6 a^2-6 from both sides:

    -4 a^2-4 a = 0

    Solve the quadratic equation by completing the square:

    Divide both sides by -4:

    a^2+a = 0

    Add 1/4 to both sides:

    a^2+a+1/4 = 1/4

    Factor the left hand side:

    (a+1/2)^2 = 1/4

    Take the square root of both sides:

    a+1/2 = -1/2 or a+1/2 = 1/2

    Subtract 1/2 from both sides:

    a = -1 or a+1/2 = 1/2

    Subtract 1/2 from both sides:

    a = -1 or a = 0

    Now test that these solutions are appropriate by substitution into the original equation:

    Check the solution a = 0:

    2/(a^2-1) => 2/(-1+0^2) = -2

    6/(a^2-2 a-3) => 6/(-3-2 0+0^2) = -2

    So the solution is correct.

    Thus, the solutions are:

    a = -1 or a = 0

  • 1 decade ago

    2/(a^2 - 1) = 6/(a^2 - 2a - 3)

    you will need to cross multiply for the denominators to be the same.

    2(a^2 - 2a - 3) = 6(a^2 - 1)

    2a^2 - 4a - 6 = 6a^2 - 6

    -4a^2 -4a = 0

    factor

    divide both sides by -4 because it is a common factor

    a^2 + a = 0

    use completing the square method

    a^2 + a +(1/2)^2 = 0 + (1/2)^2

    a^2 + a + 1/4 = 1/4

    now fully factor

    (a + 1/2)^2 = 1/4

    find the square root of both sides to remove the squared symbol

    a + 1/2 = + or - sqrt.(1/4)

    = + or - 1/2

    a = 0 or -1

  • 1 decade ago

    ok, I will just explain, since there is no good way to show work on here. start by cross multiplying.

    so 6(a^2 -1) = 2 (a^2-2a-3)

    Then distribute the 6 and the 2

    then get all numbers on 1 side so that all the a's and stuff =0

    Then we use the zero product property to solve

    you factor the a's and set the factors equal to 0

    then solve for a.

    There will be at most 2 solutions.

    Source(s): I am a math teacher.
  • 1 decade ago

    2/a^2-1=6/a^2-2a-3 first you need to factor at bottom out

    2/(a+1)(a-1)=6/(a-3)(a+1) LCD will be a+1, a-1, a-3 see another miss what LCD time that

    2(a-3)=6(a-1)

    2a-6=6a-6

    6a-2a=-6+6

    4a=0

    answer will be 0

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