2x
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(x-2)(x+2) using partial fractions
That's supposed to be a division sign of some sort
Assume
2x/((x-2)(x+2)) = A/(x-2)+B(x+2)
Right hand side
=(A(x+2)+B(x-2))/((x-2)(x+2))
=((A+B)x+(A-B))/((x-2)(x+2))
Compare denominators on both sides and equate coefficients of powers of x to get
A+B=2
A-B=0
from which A=B=1
So the decomposition into partial fractions is
1/(x+2) + 1/(x-2)