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!

Found 2 solutions by stanbon, jim_thompson5910:
Answer by stanbon(75887)   (Show Source): 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)]
==============================

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)
==========================================
Chers,
Stan H.

Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
I'll do the first one to get you started

Start with the given expression


Factor the second denominator


Simplify


So we can see that the LCD is . So we need to multiply the first fraction by to get the denominator to the LCD


Multiply the first fraction by


Combine the fractions


Multiply


Combine the fractions


So simplifies to

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