SOLUTION: Subtract (6x)/(x^2-4)-(3)/(x-2)

Question 269608: Subtract
(6x)/(x^2-4)-(3)/(x-2)
Answer by dabanfield(803) (Show Source): You can put this solution on YOUR website!
(6x)/(x^2-4)-(3)/(x-2)
To substract the trms wee need to find a common denominoater:
6x/(x^2-4) - 3/(x-2)
Rewrite the above factoring the denominator of the first term:
6x/[(x+2)*(x-2)] - 3/(x-2)
If we multiply the second term by (x+2)/(x+2), which is equal to 1 and so doesn't change the value of the term, we have:
6x/[(x+2)*(x-2)] - [3*(x+2)]/[(x+2)*x-2)]
Now that both terms have the same denominator, using the rule that a/b + c/b = (a+c)/b we can combine numerators as follows:
[6x - 3(x+2)]/[(x+2)*(x-2)] =
(3x - 6)/[(x+2)*(x-2)] =
[3*(x-2)]/[(x+2)*(x-2)] =
3/x+2)
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