Answer:
[tex]\frac{2}{x-y}}[/tex]
Step-by-step explanation:
This equation may look difficult, but let's take it step by step. We are given the equation [tex]\frac{3x+3y}{x^{2}-y^{2} } -\frac{1}{x-y}[/tex].
We can simplify this to [tex]\frac{3x+3y}{(x-y)(x+y)} -\frac{1}{x-y}[/tex] through the difference of two squares formula. Now, we need to make the denominators the same, so:
[tex]\frac{3x+3y}{(x-y)(x+y)} -\frac{(x+y)}{(x-y)(x+y)}[/tex]
We can finally combine the fractions since they have the same denominator:[tex]\frac{3x+3y - (x +y)}{(x-y)(x+y)}}[/tex]
We distribute the negative: [tex]\frac{3x+3y - x-y}{(x-y)(x+y)}}[/tex]
From here, we combine like terms: [tex]\frac{2x+2y}{(x-y)(x+y)}}[/tex]
There's still one more step, we can factor out a two from the numerator: [tex]\frac{2(x+y)}{(x-y)(x+y)}}[/tex] so that we can cancel out the term (x+y).
We are left with [tex]\frac{2}{x-y}}[/tex]
