Find all real solutions to the equation 1 - 1/(x-2) = -4/(x^2-4).

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1 - 1/(x-2) = -4/(x^2 - 4)

First we will rewrite 1 as a fraction.

==> 1 = (x-2)/(x-2)

==> (x-2)/(x-2) - 1/(x-2) = -4/(x^2 -4)

==> (x-2-1)/(x-2) = -4/(x^2-4)

==> (x-3)/(x-2) = -4/(x^2 -4)

Now we will factor x^2 -4 = (x-2)(x+2)

==> (x-3)/(x-2) = -4/(x-2)(x+2)

Now we will reduce similar terms.

==> (x-3) = -4/(x+2)

Now we will multiply by (x+2).

==> (x-3)(x+2) = -4

==> x^2 -x - 6 = -4

==> x^2 -x -2 = 0

==> (x-2)(x+1) = 0

==> x = 2 and x= -1

==> x = ( -1, 2}

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