SOLUTION: I am trying to simplify 2 fraction problems with variables and exponents, probably using factoring, but depite all the factoring I have tried, my answers don't come up with common
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-> SOLUTION: I am trying to simplify 2 fraction problems with variables and exponents, probably using factoring, but depite all the factoring I have tried, my answers don't come up with common
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Question 162413: I am trying to simplify 2 fraction problems with variables and exponents, probably using factoring, but depite all the factoring I have tried, my answers don't come up with common denominators, so the numbers don't combine. Here is the first problem:
yx^2/(x-y)+xy^3/(xy-x^2)
This is the second:
1/(a^2+b^2)+1/(a^2-b^2)+2b^2/(a^4-b^4)
Any help you can give would be REALLY awesome!
You can put this solution on YOUR website! 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
-----------------------
= (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.
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