Find the discriminant of the quadratic equation 1/x+2 + 1/x-2=2?

To find the discriminant of the quadratic equation, we first need to rewrite the equation in standard form.

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

To combine the fractions, we need a common denominator. The common denominator is (x+2)(x-2), so we rewrite the equation as:

(x-2 + x+2)/(x+2)(x-2) = 2

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

Now we can rewrite the equation in standard form:

2x = 2(x^2 - 4)

2x = 2x^2 - 8

Rearranging the terms, we get:

2x^2 - 2x - 8 = 0

Now we can identify the coefficients of the quadratic equation:

a = 2
b = -2
c = -8

The discriminant of a quadratic equation is given by the formula:

Δ = b^2 - 4ac

Plugging in the values of a, b, and c, we get:

Δ = (-2)^2 - 4(2)(-8)
Δ = 4 + 64
Δ = 68

Therefore, the discriminant of the quadratic equation 1/(x+2) + 1/(x-2) = 2 is 68.