SOLUTION: combine and simplify:
3x/(x+2) + x/(x-2) - 4x/(x^2-4)
the answer is 4x/(x+2), but I can't figure out how to get it.
Algebra.Com
Question 553022: combine and simplify:
3x/(x+2) + x/(x-2) - 4x/(x^2-4)
the answer is 4x/(x+2), but I can't figure out how to get it.
Answer by TutorDelphia(193) (Show Source): You can put this solution on YOUR website!
Like all fraction addition, the first thing we have to do is get the denominators the same.
Your teacher gave you a problem that works out relatively easily if you know the trick. The trick is the (x+2)*(x-2)=x^2-4. This is called the difference of two squares and you can find more info on it here: http://www.themathpage.com/alg/difference-two-squares.htm
So my common denominator will be x^2-4
To get the first fraction to equal that on the denominator I have to multiply by (x-2), for the second fraction, I have to multiply by x+2 and the third is already set
I can distribute the bottoms and get:
Since the denominator is all the same, I can now add or subtract the tops:
Distributing the tops gets me
Combining like terms:
Let's factor out a 4x from the top
now remember
the x-2 cancels out and we get
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