Question 45068
x over 4 - 4 over x =0 

x/4 - 4/x = 0
x^2-16=0
(x-4)(x+4)=0
x=4 or x=-4
-----------------------------

1 over x+3 + 1 over x-3 = 1 over x^2-9

1/(x+3) +1/(x-3)=1/(x^2-9)

Multiply through by x^2-9 to get:
x-3 + x+3 = 1
2x=1
x=1/2
-----------------------------------
x over x+4 - 4 over x-4 = x^2+16 over x^2-16

x/(x+4) - 4/(x-4) = (x^2+16)/(x^2-16)

Multiply thru by x^2-16 to get:

x(x-4) - 4(x+4) = x^2+16

x^2-8x-4 = x^2+16
-8x-4=16
-2x-1=4
-2x=5
x=-5/2
-------------------------------
y^2-4 over y+3= 2 - y-2 over y+3

(y^2-4)/(y+3) = 2 - (y-2)/(y+3)

Multiply both sides by (y+3) to get:

y^2-4 = 2(y+3) -(y-2)
y^2-4 = 2y+6-y+2
y^2-y-12=0
(y-4)(y+3)=0
y=4 or y=-3
----------------------
Cheers,
Stan H.