find the LCD?

Question

Find the LCD

4/x-y , 5x/2y-2x

Answer 1

(4/(x - y)), ((5x)/(2y - 2x))
(4/(x - y)), ((5x)/(-2x + 2y))
(4/(x - y)), ((5x)/(-2(x - y))

LCD = -2(x - y)

Answer 2

When looking for the LCD, you are trying to find the smallest quantity that both denominators will divide evenly into.

the two denominators are x - y and 2y - 2x
Most algebraic problems are greatly simplified by factoring polynomials that you can factor. Then we can more easily see similarities between two or more polynomials

x-y does not factor. But 2y-2x does factor.

2y - 2x = 2(y - x)

now the two denominators look like they have more in common.
It would be great if the (y -x ) were (x -y) instead.

So factor it like this : -2 ( x - y)
Now we can match up the two denominators we were given and see that the LCD in this case is -2( x - y)