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

RELATED QUESTIONS

combine and simplify: 6/x + 7/x^2 the correct answer is x^2(6x+7), but I can't... (answered by Earlsdon)
Hello, I know the answer is 14 to the following problem but I can't figure out how to... (answered by jim_thompson5910)
Here is the multiple choice question: Simplify... (answered by MathLover1)
12^2+17x+6=___? A. (3x+2)(4x+3) B. (3x-2)(4x-3) C. (12x+2)(x+3) D. (12x+1)(x+6)... (answered by longjonsilver)
f(x)=x^2+1 find for f(x+2) f(x+2)=(x+2)^2 +1 =x^2+4+1 =x^2 +5 But book... (answered by nerdybill)
Find a polynomial f(x) of degree 3 that has the indicated zeros and satisfies the given... (answered by Alan3354)
Simplify the following expression: 11x^2(11-3x)/4x(3x-11)= What I've done so far: (answered by Alan3354)
How do I simplify this problem and the steps for it. x^2-4x+2xy-8y I know that the... (answered by Nate)
regarding algebra factorising: question is 4X + 8 = 4(X + 2) i was given this question (answered by RAY100)