If I am reading the problem correctly, we have:
1/(2x - y) - 2/(x + 2y)
The LCD would be (2x - y)(x + 2y)
What's missing from the first term? There's no (x + 2y) term in the denominator, so we multiply top and bottom of that term by (x + 2y). That gives us:
[1(x + 2y)]/[(2x - y)(x + 2y)] = [x + 2y]/[(2x - y)(x + 2y)]
What's missing from the second term? There is no (2x - y) in the denominator. Multiply top and bottom by (2x - y). We will have:
[2(2x - y)]/[(2x - y)(x + 2y)] = [4x - 2y]/[(2x - y)(x + 2y)]
Now that we have a common denominator, we can combine the numerators of the two terms:
x + 2y - (4x - 2y) = x + 2y - 4x + 2y = 4y - 3x
So the difference of these two terms will be:
[4y - 3x]/[(2x- y)(x + 2y)]
