SOLUTION: find: 2x/(x^2-9) + (1-2x)/(x^2-4x+3)

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Question 232845: find:
2x/(x^2-9) + (1-2x)/(x^2-4x+3)
Answer by eggsarecool(46) About Me  (Show Source):
You can put this solution on YOUR website!
I am assuming you want this solved for 0
2x%2F%28x%5E2-9%29+%2B+%281-2x%29%2F%28x%5E2-4x%2B3%29=0 So first we need a common denominator
We will start by factoring the current denominators.
2x%2F%28x%2B3%29%28x-3%29%2B%281-2x%29%2F%28x-3%29%28x-1%29=0
Now for the common denominator.
Now your denominator cannot equal to zero since you are not allowed to divide by 0. so x cannot equal to 1, 3, or -3.
Since the bottom cannot equal 0 the only time the fraction will equal 0 is when the numerator equals 0.
Now we multiply out the numerator.
%282x%5E2-2x%2Bx%2B3-2x%5E2-6x%29%2F%28x%2B3%29%28x-3%29%28x-1%29=0
Next we combine like terms.
%28-7x%2B3%29%2F%28x%2B3%29%28x-3%29%28x-1%29=0
Now we set the numerator equal to 0 and solve.
-7x%2B3=0 Add 7x to both sides.
7x=3 Divide both sides by 7.
x=3%2F7