Answer:

To simplify the expression (x³+y³)/(x³-y³) multiplied by (x-y)/(x+y), we first need to factor the numerator and denominator of each fraction.

For the first fraction, we can use the difference of cubes formula to factor the numerator and denominator:

(x³+y³)/(x³-y³) = [(x+y)(x²-xy+y²)]/[(x-y)(x²+xy+y²)]

For the second fraction, we can factor out a negative sign from the denominator:

(x-y)/(x+y) = -(y-x)/(x+y) = -1(y-x)/(x+y)

Now we can simplify the expression by canceling out common factors:

[(x+y)(x²-xy+y²)]/[(x-y)(x²+xy+y²)] * -1(y-x)/(x+y)

Next, we can cancel out the (x+y) terms:

(x²-xy+y²)/[(x-y)(x²+xy+y²)] * -1(y-x)

Finally, we can simplify further by rearranging the terms:

-(x²-xy+y²)(x-y)/(x²+xy+y²)(y-x)

Note that we can cancel out the (y-x) terms as well, giving us the simplified expression:

-(x²-xy+y²)/(x²+xy+y²)