Question 162413
Here is the first problem: 
yx^2/(x-y)+xy^3/(xy-x^2)

= yx^2/(x-y)+xy^3/(-x(x-y))

The LCD = -x(x-y)

= -yx^3/lcd + xy^3/lcd

= [-yx^3 + xy^3]/lcd

= [-xy(x^2 - y^2)]/[-x(x-y)]

= [y(x + y)]
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This is the second: 
1/(a^2+b^2) + 1/(a^2-b^2) + 2b^2/(a^4-b^4) 

lcd = a^4 - b^4
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= (a^2 - b^2)/lcd + (a^2 + b^2)/lcd + 2b^2/lcd

Add the three numerators to get:

= (2a^2 + 2b^2)/lcd

= [2(a^2+b^2)] / [(a^2+b^2)(a^2-b^2)]

= 2/(a^2-b^2)
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Chers,
Stan H.