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Do the indicated operations, express your answers in lowest terms

Do the indicated operations, express your answers in lowest terms-example-1

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8 votes

Answer:


(2)/(x-y)}

Explanation:

This equation may look difficult, but let's take it step by step. We are given the equation
(3x+3y)/(x^(2)-y^(2) ) -(1)/(x-y).

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


(3x+3y)/((x-y)(x+y)) -((x+y))/((x-y)(x+y))

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

We distribute the negative:
(3x+3y - x-y)/((x-y)(x+y))}

From here, we combine like terms:
(2x+2y)/((x-y)(x+y))}

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

We are left with
(2)/(x-y)}

User David Cuthbert
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