SOLUTION: 1. x over 4 - 4 over x =0 2. 1 over x+3 + 1 over x-3 = 1 over x^2-9 3. x over x+4 - 4 over x-4 = x^2+16 over x^2-16 x over x+4 - 4 over x-4 = (x+4)(x+4) over

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: 1. x over 4 - 4 over x =0 2. 1 over x+3 + 1 over x-3 = 1 over x^2-9 3. x over x+4 - 4 over x-4 = x^2+16 over x^2-16 x over x+4 - 4 over x-4 = (x+4)(x+4) over       Log On


   

Question 45068: 1.
x over 4 - 4 over x =0


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


3.
x over x+4 - 4 over x-4 = x^2+16 over x^2-16

x over x+4 - 4 over x-4 = (x+4)(x+4) over (x-4)(x+4)

LCD= (x+4)(x-4)

x over x+4 * (x-4) over (x-4) - 4 over x-4 * (x+4) over (x+4) = (x+4)(x+4) over (x-4)(x+4)

x(x-4) over (x+4)(x-4) - 4(x+4) over (x+4)(x-4) = (x+4)(x+4) over (x-4)(x+4)

x(x-4)-4(x+4)=(x+4)(x+4)

A little stuck here
x^2-4x-4x-16=x^2+8x+16
x^2-8x-16=x^2+8x+16
(x-4)(x-4)=(x+4)(x+4)

4.
y^2-4 over y+3= 2 - y-2 over y+3
y-2 over y+3 is one faction
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
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
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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
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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
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Cheers,
Stan H.