Perform the indicated operations and reduce all results to lowest terms. Assume the variables are restricted to values that prevent division by 0.

Question

(x^2-y^2)/(x^2-2xy+y^2) divided by (3x+3y)/(7x-21)

Could someone please show me how to do this so I can do the rest of my homework? I don't understand this at all. Thank You

Answer 1

(x^2-y^2) = (x+y)(x-y)
x^2-2xy+y^2 = (x-y)(x-y)
so when you divide the first by the second you get
(x+y)/x-y)

Now work on the bottom
(3x+3y) = 3(x+y)
(7x-21)= 7(x-3)

Now turn that upside down and multiply by the numerator
7(x-3) /3(x+y) * (x+y)/(x-y)

(7)(x-3)/3(x-y)

Answer 2

-1(y+6)+3(y+1)+7y