Question 269608
(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)