Question 607640
{{{(x-2)/(x^2-4) + 2/(x+2)}}}
{{{(x-2)/((x+2)(x-2)) + 2/(x+2)}}}
{{{(x-2)/((x+2)(x-2)) + (2/(x+2))((x-2)/(x-2))}}}
{{{(x-2)/((x+2)(x-2)) + (2x-4)/((x+2)(x-2))}}}
Everything you've done so far is correct. The reason you found the LCD and changed the second fraction so it had the LCD for a denominator was so you could add the fractions. So that is the next step, add:
{{{(3x-6)/((x+2)(x-2))}}}
Now, as usual when you have a fraction for an answer, we reduce the fraction if possible. To reduce a fraction you cancel common factors in the numerator and denominator. To cancel common factors you have to have factors, first. The denominator is already/still factored. In the numerator we have a GCF of 3 we can factor out:
{{{(3(x-2))/((x+2)(x-2))}}}
And lo and behold, we have a common factor of (x-2) we can cancel:
{{{(3*cross((x-2)))/((x+2)*cross((x-2)))}}}
leaving:
{{{3/(x+2)}}}
which will not reduce further.