Question

Do the indicated operations, express your answers in lowest terms

Answer 1

Answer:

$\frac{2}{x-y}}$

Step-by-step explanation:

This equation may look difficult, but let's take it step by step. We are given the equation $\frac{3x+3y}{x^{2}-y^{2} } -\frac{1}{x-y}$.

We can simplify this to $\frac{3x+3y}{(x-y)(x+y)} -\frac{1}{x-y}$ through the difference of two squares formula. Now, we need to make the denominators the same, so:

$\frac{3x+3y}{(x-y)(x+y)} -\frac{(x+y)}{(x-y)(x+y)}$

We can finally combine the fractions since they have the same denominator:$\frac{3x+3y - (x +y)}{(x-y)(x+y)}}$

We distribute the negative:  $\frac{3x+3y - x-y}{(x-y)(x+y)}}$

From here, we combine like terms: $\frac{2x+2y}{(x-y)(x+y)}}$

There's still one more step, we can factor out a two from the numerator: $\frac{2(x+y)}{(x-y)(x+y)}}$ so that we can cancel out the term (x+y).

We are left with $\frac{2}{x-y}}$