Question 324884
The LCD stands for the lowest common denominator. You can easily find the LCD by first multiplying all the denominators together and then dividing that product by the GCF (greatest common factor)


Step 1) Find the GCF of the denominators: Take note that {{{2y-2x=-2(x-y)}}}. So {{{x-y}}} is a common factor between the first denominator {{{x-y}}} and the second denominator {{{2y-2x}}}. The two denominators have nothing else in common. This means that the GCF is {{{x-y}}}



Step 2) Multiply the two denominators: {{{(x-y)(2y-2x)}}} You can go further and FOIL it out, but it's not necessary.



Step 3) Divide the result of step 2 by the GCF: {{{((x-y)(2y-2x))/(x-y)=(cross((x-y))(2y-2x))/cross((x-y))=2y-2x}}}




So the LCD is {{{2y-2x}}}