So firstly, we will be using the difference of squares with the second fraction's denominator. The difference of squares is [tex] x^2+y^2=(x+y)(x-y) [/tex] . Apply this rule to this expression: [tex] \frac{3}{x+4}+\frac{2}{(x+4)(x-4)} [/tex]
Next, we have to find the LCM, or least common multiple, of both denominators. In this case, the LCM is (x + 4)(x - 4). Multiply the denominators with the quantity that gets the LCM as the denominator, and then multiply by that same amount on their numerators:
[tex] \frac{3}{x+4}*\frac{(x-4)}{(x-4)}=\frac{3(x-4)}{(x+4)(x-4)}\\ \\ \frac{2}{(x+4)(x-4)}*\frac{1}{1}=\frac{2}{(x+4)(x-4)}\\ \\ \frac{3(x-4)}{(x+4)(x-4)}+\frac{2}{(x+4)(x-4)} [/tex]
Now foil 3(x - 4): [tex] \frac{3x-12}{(x+4)(x-4)}+\frac{2}{(x+4)(x-4)} [/tex]
And lastly, add the numerators up and your final answer will be [tex] \frac{3x-10}{(x+4)(x-4)} [/tex]
