Find the LCD?

Question

convert the rational expression into an equialent rational expression with LCD as the denominator

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

Answer 1

4 / (x - y) and 5x / [ (- 2) (x - y) ]
becomes
(- 8) / [ (- 2) (x - y) ] and 5x / [ (- 2) (x - y) ]
These expressions may be added to give:-
(5x - 8) / [ (- 2) (x - y) ]

Answer 2

To find the LCD of rational expressions, it is best to factor the denominators first to see if there are any common parts. The first expression cannot be factored any, but the second one can be broken down into,
5x/[2(y - x)]
At this point, there is a slight relationship between this denominator and the first, but the letters are backwards. To flip them around, factor out -2 instead of just 2. Doing this you get,
5x/[-2(-y + x)]
Rewriting -y + x, you should get,
5x/[-2(x - y)]
Now you can see that the denominators have x - y in common. So, the LCD is simply -2(x - y). Thus,
4/(x - y) = (-2)(4)/[-2(x - y)] = -8/[-2(x - y)] or -8/(2y - 2x).
That should do it for you. Hope this helped.