1/x-2=3/x+2 -6x/x^2-4

Question

Solve this problem

Answer 1

Hi Zach,

 

We'll solve our equation step-by-step:

    1.  Original equation:

             1/(x-2) = 3/(x+2) - 6x/(x²-4)

    2.  Get linear terms together on one side:

             1/(x-2) - 3/(x+2) = -6x/(x²-4)

    3.  Get common denominator on left side:

             [(x+2) - 3(x-2)]/(x-2)(x+2) = -6x/(x²-4)

    4.  Simplify common denominator on left side:

             [(x+2) - 3(x-2)]/x²-4 = -6x/x²-4

    5.  Multiply both sides by like denominator:

             [(x+2) - 3(x-2)] = -6x

    6.  Distribute left side:

             x + 2 - 3x + 6 = -6x

    7.  Combine like terms on left side:

             -2x + 8 = -6x

    8.  Combine like terms on both sides:

             -2x + 6x = -8

    9.  Solve for x:

             4x = -8

               x = -8/4

               x = -2

 

Finally, let's check our answer by plugging it back into the original equation and see if both sides balance:

    1(x-2) = 3(x+2) - 6x/(x²-4)

    1/(-2-2) = 3(-2+2) - [6(-2)]/[(-2)²-4]

    -(1/4) = 3/0 + 12/0 (undefined)

 

No Solution (answer yields undefined equation !!)

 

Thanks for submitting this problem and glad to help.

 

God bless, Jordan.