four divided by the difference of a number and 2 ​, minus 3 divided by a number plus 2​, equals 8 times the reciprocal of the difference of the number squared and 4 .

Answer 1

4(x-2) -3/x + 2 = 8(1/(x^2 - 4)

4x - 8 -3/x + 2 = 8/(x^2 - 4)

4x -3/x -6 = 8/(x^2 -4) eliminate the fractions by multiplying by x(x^2-4)

4x^2(x^2-4) - 3(x^2-4) - 6x(x^2-4) = 8x

4x^4 -16x^2 -3x^2 +12 -6x^3 +24x = 8x

4x^4 -6x^3 - 19x^2 +16x + 12 = 0

this is a 4th degree polynomial with 4 real solutions

Graphically it's a "W" shape with 3 turning points, and the "W" intersects the x axis 4 times

at between x=-3 and x=-2

between x=-1 and x=0

between x = 1 and x=2

and between x=2 and x=3

Just a very rough approximation might be

x=-2.5, -0.5, 1.5 and 2.5

This is an attempt to interpret the problem using PEMDAS, the order of operations where parentheses come first, then exponents, then multiplication, then division, then addition, and last subtraction. But the wording of the problem is ambiguous enough, it could be interpreted other ways.