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Transcript 
Simplify
y2 /X2 - 4y2 + y/2x + 4y
Answer:
First we must write this equation properly as follows
(y2/x2 – 4y2) + (y / 2x + 4y)
The common denominator between the two terms is (x2 – 4y2)(2x+4y). Now if we put the equation in terms of the
common denominator, we have
[(y2 (2x+4y)) + (y(x2 – 4y2)]/( x2 – 4y2)(2x+4y)
Now if we multiply everything out, we have
(2xy2 + 4y3 + x2y – 4y3) / (2x3 + 4x2y – 8xy2 – 16y3)
This now equals
(2xy2 + 4y3) / (2x3 + 4x2y – 8xy2 – 16y3)
= (2xy2 + 4y3) /
[ 2x2 (x+2y) – 8y2 (x+2y)]
= (2xy2 + 4y3) / [(2x2 – 8y2)(x+2y)]
= 2y2 (x + 2y) / [(2x2 – 8y2)(x+2y)]
The x+2y term will now cancel out and we are left with
= 2y2 / (2x2- 8y2)
= 2y2 / 2(x2- 4y2)
= y2 / (x2- 4y2)
= (y2 /x2) – (y2 / 4y2)
= (y2 /x2) – (1 / 4)
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