Question:
In general, I understand rational expressions except when it comes to solving problems such as:

x+y/2x-y - 2x/y-2x or m-4/3m-4 + 3m+2/4-3m

I am confounded by the issue of having to find a common denominator. For example, if I tried to solve these problems by multiplying both denominators they would still be uncommon. I hope these problems can be expounded on as much as possible. Thank You!

Hi,

The first problem is

x + ^y/_2x - y - ^2x/_y - 2x

The two denominators are 2x and y so a common denominator is 2xy. Expressing each term with denominator 2xy I get

 ^2x2y/_2xy + ^y2/_2xy - ^2xy2/_2xy - ^4x2/_2xy - ^4x2y/_2xy

= ^{(2x2y + y2 - 2xy2 - 4x2 - 4x2y)}/_2xy

= ^{(-2x2y +y2 -2xy2 - 4x2)}/_2xy

(P.S. I hope you did not mean something like

 ^(x+y)/_2x - ^{(y - 2x)}/_(y-2x)

and forgot the parentheses.)

Claude

Go to Math Central