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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