Question 204353: I need help with this rational expression please. I am supposed to find the LCD and convert it into an equvalent rational expression with the LCD as the denominator:
4/(x-y),5x/(2y-2x)
Here's my try: The LCD is 2(x-y)
answer: 8x-8y/2(x-y)
10x^2-10xy/2(x-y)
Thanks
Answer by jsmallt9(3758)   (Show Source):
You can put this solution on YOUR website! 4/(x-y),5x/(2y-2x)
Since there is a comma and not an operator I am not sure what to do here. But since you mention LCD and LCD's are only needed for addition and subtraction, I'll guess... subtraction (the harder one)"
To avoid possible difficulties, I'm going to change the "big" subtraction into addition:
Now, to find the LCD. First, factor the denominators as completely as possible:
Next, look for comon factors. At first it looks like there are none. But it is helpful to realize that (x-y) = -1(y-x). So if we factor out a -1 we will have a common factor. (If you don't factor out the -1, then you scan still get the problem correct. But it will be more difficult.)
Factored this way our LCD is (-2)(x-y). (Without factoring the -1, the LCD would be (2)(x-y)(y-x).)
Next we mulitply the numerator and denominator of each fraction by any factors of the LCD if is "missing":
The second fraction is not "missing" any factors. so we leave it as it is. Since we will be trying to reduce the fraction at the end, it is best to leave the denominators factored.
Now we can add:
The only reducing which can be done is to factor out a -1 and cancel it. (If you did not factor out -1 earlier, then you have more serious factoring and reducing to do at this point):
Simplifying the denominator:
{If we were supposed to add instead of subtract, the answer would be:  )
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