Question 189446
Simplify:
{{{(2/(x-2))+(3/(x+2))-(x+6)/(x^2-4)}}}
Find the common denominator: {{{(x-2)(x+2)= (x^2-4)}}}
Multiply the first fraction by {{{(x+2)/(x+2)}}} and the second fraction by {{{(x-2)/(x-2)}}}
{{{(2(x+2)/(x-2)(x+2))+(3(x-2)/(x+2)(x-2))-(x+6)/(x^2-4)}}} Simplify:
{{{((2x+4)/(x^2-4))+((3x-6)/(x^2-4))-((x+6)/(x^2-4)) = (4x-8)/(x^2-4)}}} Now factor 4 from the numerator and factor the binomial in the denominator.
{{{4cross((x-2))/cross((x-2))(x+2)}}} Cancel the indicated factors to leave you with:
{{{highlight(4/(x+2))}}}